I am CEO and co-founder at control plane. We are a cloud native security consultancy We do security audits pen testing consulting and love to run cap to the flag events We do those at kubecon every six months or so If you find yourself at the security con prior to kubecon coming up in Detroit, please come and play one of our carefully constructed games I've done various things. I'm proud to be involved with the CNCS tag security and Also do some work for open UK advocating for open source and trying to keep up with the Pace of open source Awareness that the the US Biden administration is showing great leadership in at the moment I've also written a book recently with my esteemed friend and colleague mr. Michael Hassenblas the first half of the book is available as a free PDF download Which slightly edges the the printed book because you can just copy and paste the examples it is written with hacks and Yolo techniques for your q and at his clusters and Details everything from insider pods out to compromising a node a cluster and ultimately your cloud environment So today we are going to talk about trust in the context of secrets management and access control Focusing primarily on machine identity What it is how we get one Talk about some things that hopefully will be interesting and slightly new and Hopefully things that you can take back and use in the context of your day jobs So with that where did we come from before cloud? without needing to possess any primary secret material or Any knowledge of their own identity We want identity documents that are short lived the equation the acquisition and replacement of them has to be simple and We want this to be seamless for our workloads of course Finally, we need a way for the relying parties to verify these things are correct and the identity documents are valid So ideally the basis of course for this is cryptography The format of choice for these identity documents in the modern age is JWT's or Jots and x509 certificates So now we're sold on this concept. How do we get one? We start with something simple that we probably already know Who's running workloads on Kubernetes? Yeah, the majority good and who has heard of the token review API a few less. Yeah Okay, so we'll dig into this now Here we have two service accounts Each one has a token The subject makes a request it sends that token in an authorization header And it uses a secure channel like TLS to protect against interception and replay The relying party then makes a call to the Kubernetes API server sending In that cryptographic looking string Does anybody know the serialization format for Jots? It's a bit bizarre when you base 64 decoder. It doesn't quite spit out properly There is a header payload and a signature. It's base 64 and URL encoded separated with a period halfway through So we can pipe this through jq like this and have a look at the payload or the header We can't decode the signature as it's not utf8 But generally we're only interested in the payload and possibly the header No more pasting tokens into JWT.io. It's probably not a good idea So this is the decomposition of We see here the header. We have the algorithm Then we see metadata about the pods and the service accounts and the subject there at the bottom We have a lot of metadata in here as well The json web key sets URL So this is a set of keys containing the public keys used to verify any Jots Issued by the authorization. So the EKS payload looks very similar indeed Of course because it's a standardized format, but we have a different issuer That is not static that will change and The discovery document that goes with it and again the EKS JSON web key set Nothing particularly different in there one difference here with a rather as it mentions This defines a standard for an identity framework Spire is a concrete implementation And these technologies have been going round for a number of years now Istio implements some form of the spiffy standard it's Neither complete nor Absolute but still goes in the right direction Exchanging identity for cryptographic material that can be used not only for authorization, but also mutual TLS So for spiffy, we are defining the format of an identifier as a uri You can see here the spiffy identity spiffy at the dot-com billing payments for example This is baked into an SFID spiffy verifiable identity documents This is then used to for example generate an X509 or a Jots Which means that it's cryptographically verifiable in various different ways it can be short-lived and rotated frequently and Yeah, as I say that there's multiple different mechanisms for that SFID to be bundled into the trust domain Just provides the bundle and the root keys to verify the SFID the workload API then defines a protocol by which to securely retrieve and verify the SFID which gives us the ability to Not only mint and generate these certificates But then those certificates can be used to mutually identify each other when there is a shared root root of trust or shared public key So how does this work because there's various different implementations One of the ways is to run a node agent. So a trusted process sat Running his roots on a node Observing the workloads that are created as unprivileged or processes owned by unprivileged users on same node and Then attesting their identity against the server exchanging metadata about those processes with the server, which is then minted into a certificate, which is returned given to the process and used to bootstrap that workload identity and to also maintain encrypted communication Workloads attest themselves to the agents and the registration maps Selectors containing metadata specific to the attestation to spiffy IDs And a parent spiffy ID for workload maps workloads on the node So that we know which workloads are allowed to run in which nodes Workloads can then use the workload API to get their SFIDs This is not the only way that we can attest to identity We can also on the left-hand side the node based attestation Agent server so those top three mechanisms utilize shared secrets, but we also have kubernetes We also have cloud identity documents. So this concept of running a privileged agent process Incidentally, this is all threat modeled the security properties of published tag security did a review of this a couple of years ago And the glass radius of various different types of compromise. It's all available to download in the tag security archives The principle of having a trusted node agent means that the compromise of that node Means an attacker can then mint certificates based upon arbitrary falsified metadata So there are other ways to do this as well Of course that limits the blast radius to the workloads that are permitted to run on that node type But by extension some of these cloud provider integrations Use metadata about a virtual machine. So instead of having a trusted node at the attestation process on every node on every virtual machine on every cubanet on every cubelit in the cubanet cluster When attesting to cloud infrastructure We run that on one dedicated node that uses the AWS or the GCP APIs to retrieve metadata about the virtual machines That's what's then used as the metadata in the selectors to generate the certificates And that's what's then pushed to the machines to be used as the basis of identity So this can be done in other ways for the sake of simplicity. I think especially the way that Istio implements this this style is again not with a node attester But going directly to the cubanet is API. So there's multiple different ways to the skin and slice this Ultimately the implementation that makes the most sense is dependent on your threat model, of course We can also do individual workload attestation here We can use Unix identifiers like user IDs or process names Use group IDs and names the path to a processes binary the digest of that binary Can use for a container the image ID? labels environment variables if we so choose and of course in cubanet is service counts namespaces images, etc Then on a single cubanet is cluster by extension. We can use the projected service account token node attestation We're back to the token review API at this point, which is the same as the vaults authentication method earlier and We then also have the idc discovery provider exposing our endpoints to retrieve the doc the discovery documents and the jwks url as It's oidc discovery. It just looks the same as the previous examples And we can use it in the same way as a cubanet is service account jot So far we have focused just on the Jots Motivation for this was to demonstrate that we can do a lot with cubanet is as our IDP as our identity provider spy gives us extra capabilities, but with an Administrational and operational overhead You get these for free on cubanet is again There was a balance here of operational versus risk The specific use case will determine your need But the assumption is for some of this that a service mesh is used for secure communication Or at least a mutual TLS exchange Or indeed just a one-way TLS exchange as long as there is Encryption that prevents the provisioning of these tokens being intercepted obviously What if we want the same workload ID in the Jots and the x5 and 9? Well, we can also provide the Svid is the x5 and 9 document where the spiffy ID is in the URI SAN the subject alternative name Then we can use for server and client authentication the certificate be used for mutual TLS to log into vaults Or for anything else that supports certificate based authentication When we're using this to log into vaults the question of having a key to unlock the box to get the second key out It's fixed because the workload is provisioned a cryptographic identity that it can go to vault and say hi I'm allowed to do this vault can then go out of band to the cubanet is API server Or indeed just trust the fact that this is encrypted and encoded into a certificate with a shared public key that's trusted and Give that secret zero this is Easier and more stable in my opinion than a lot of the other vaults unlock mechanisms And doesn't necessarily require so much Sort of sidecar mounting as we may have seen So get as we say Spire is also implementing the envoy secret discovery service So from a from an envoy perspective and then by extension sort of service mesh and Istio We can integrate with envoy for TLS I'm just push that directly into envoy and optionally open for policy-based access control using the spiffy IDs Okay We've looked about the software now perhaps into the hardware We'll briefly go through and I realize there are People in the room for whom this is a specialist subject. So I won't go too deep into it An indication of where it looks like workflow identity is heading for the rest of us This is towards trust at the hardware level. This is anchoring and ideally what we're looking at from a supply chain perspective is anchoring from the git commit that we make and The cryptographic material that we attach to that commit through into our build system through interstitially and sort of inter build stage Gathering of signatures with something like in toto tecton chains. We'll do some of this for us today Bundling up those signatures into an artifact which we can then sign with something like cosine Notary V2 will do some of these things as well that then gets pushed to a Kubernetes cluster where admission control says Okay, I trust this signature I can also unbundle all of the other signatures sort of been pushed as metadata alongside this container and We've got a chain of trust from the GPG key the developer used or the SSH key that they used initially I think sign and git commits is a good thing, but I realize our benevolent leader doesn't necessarily agree But yes, indeed signing all of those commits validating all the signatures and then we have an artifact that Is immune to some forms of attack Obviously a malicious insider is still not prevented by the style of attack But we are preventing build stage tampering and we're increasing the trust and the veracity of that build as it moves to production And it's finally deployed But what about that workload as it sits in production? We have trusted platform modules. We have cryptographic devices. We have trusted execution environments that take us further into the space so We're looking at secure generation and storage of keys that never leave a trusted platform module unencrypted This property allows us to tie things to a specific TPM as compromised keys cannot be reused in another TPM We also have this concept of PCRs platform configuration registers That can be read but not directly written and as values are extended We have a new hash which is comprised of a previous hash plus a measurement offset And change that hash value This goes a long way to preventing faking and tampering It's likely that PCRs could well be used for access station in the future and key lime gives or uses IMA measurements stored in those PCRs Which is the integrity measurement architecture this gives it the ability to continuously verify the integrity of remote machines and we can In this case do things like automatically remove a compromised SCD node from a cluster when we detect that there has been The integrity is compromised in some way it is worth noting that The trusted execution environments and enclaves that were shipped in consumer grade CPUs are being discontinued in the main Intel have pulled them from the latest generation of processors comparing contrasts Google put TPMs into every every VM that they have on on Google Cloud I think they kind of announced that maybe four or five years ago So this is something that's actually more difficult to do With a modern CPU than it is with a cloud provider, which is strange for something that's hardware anchored, but but there we go Okay, so we also have trusted platform module device ID attestation we can these are provisioned out of band Attestation uses the encrypted keys Which are loaded into TPM and Includes a challenge that can only succeed with the correct keys on the correct machine It's tied to the TPM so it can't be impersonated Even if the keys are compromised and it uses a fingerprint of the certificates like x509 so the default spiffy ID is predictable This dream of anchoring everything end-to-end from Commit through to the runtime attestation anchoring the process to a specific node through the TPM Still has a bit of a way to go. There's lots of moving parts But everything you've seen here is open source with the exception of the microcode in the TPM And we're certainly moving towards a brighter future where Hopefully we can see these kind of things in production within the next six to 18 months perhaps So with that You might already have a workload identity that satisfies your use case. There are plenty of other flavors Kubernetes could well be your IDP if you wish it to be Service count tokens bound service count tokens are becoming the default There is a nuance of bound service count tokens, which is Because they're temporarily bound because they have this Time time out and these usage criteria base temporal usage criteria They're pushed into a pod on a tempFS partition by the cubelets and then they're rotated If your application does not reread them from disk every time they used your process will start read its configuration and When that key is rotated it will keep on using the old Cryptographic information that are pulled at boot time So applications need to be updated in order to use bounds projected service count tokens Various different implementations. I mean you could either just read that from disk every time You could have a I notify watch on the thing as well and just pull it when it changes But it's unfortunately not just a drop-in change Of course the cure channel for communication is is a deregur Consider spiff inspire and the next generation of trusted platform modules and key lime are very exciting and looking forward to deploying them and With that, thank you very much for your attention. It was in that case Thank you very much


Electro-optic modulators can be useful for imaging, sensing and information processing applications. Here the authors demonstrate an ultra-low drive voltage visible to near-infrared range electro-optic modulator in the form of amplitude and phase modulation using thin film lithium niobate. This article was offered by Dylan Renault, Daniel Ramoli Assumpka, Graham Joe, and others.


Everybody kind of like make some noise here. Let's make some noise. There we go. But to be able to see your faces in real life and hug you and shake your hand just, it really means the world to me because when I started this little old YouTube channel about seven years ago now, I had no idea what it would turn into. I just wanted to make videos about adventures in the hopes of inspiring you to get off your couches and to get out there. And for many years not many people watched my videos. Just my mom and my brother and a few others and they're back there. Hi mom and brother Ethan. Yeah. Now I have kind of a big channel. I mean it's not huge but it's like way bigger than I ever thought it would be which is incredible and it's all because of you. So thank you for watching my videos every Sunday morning at 8 a.m.


If you drop an SCP-3008-2 inside of a backroom store level that looks like an Ikea, will they behave normally? Just like inside of SCP-3008? Backroom shower thoughts. Can you drop a baby and have it fall through the floor into the backrooms? Or is there an age and weight limit for people that can be sent there? If you un-alive in the backrooms, do you get sent back to reality? Or is that literally just the end of the road for you? Does time actually work in the backrooms? Or will you never age and be forced to look the same for eternity until an entity eats you or something? Delta says, if you escape the backrooms, do you go back to the exact point where you entered it? Or does all the time that you go through in the backrooms count as real-life time too? And if you escape, will you have been missing for years? Let me know some of your shower thoughts in the comments below.


This is amazing. Are you seeing this?  So wear underwear. So thanks to everyone who commented on the first video and asked to do the second video. So I did the first coat of resin in the past video over top of these leaves, and they still look nice. Now what I did is I sanded down all of the high peaks where the edges of the leaves kind of stuck up. So it's been sanded, so it looks rough, but don't worry when I resin the next coat, the second coat, it's gonna become perfectly clear again. So no need to worry. Grab some black, black, black. So what I'm gonna do actually, is I just have all these acrylic paints, and some inks as well. I'm just gonna add highlights of colors, especially in some gaps that were created because the leaf stuck up and then I sanded this. I'm just filling it up with acrylic paint and just all these different colors. So then we'll actually have leaves, resin, paint, then another coat of resin. So that will create a bit of a 3D effect. So let's just do it. No real science here. I'm just applying color and removing some of it. My favorite studio tool is paper towel. I would Bob Ross say it. Put a happy little cloud in here, some yellow. Lights like that, flick and flick. See, look at that. Look at those happy little splashes there. Now here's a nice mild yellow. Makes you wanna cry. It's so beautiful. Get. All right, we'll skip that one. On to pink. Ah, this is like a fluorescent pink. Holy moly, too much of that, three. This, returning to. Well, I'm not right here, baby. Look at that. But you don't have any gold. Oh, I have gold. What do you mean too bad? We don't have any gold. Put some gold in that sucker. Hell yeah, we will. Don't worry, we'll get to your gold bag. Take some gold. Is that good? Markers, pencil crayons, pastels. Ah, ooh, powders. Let's just say it's done, it's done. There, so we'll let this dry at least 24 hours with all acrylics and inks. Oils you wanna let dry a lot longer because they can keep you acting with the resin. So we'll come back and we'll apply the final coat over this and then it should be a finished work of art that was three years in the making. So, thanks for watching. Look at that. That's colorable. Is it? Whoa, that was a bit overkill.


We are under the lights as the show gets you ready for another edition of Major League Baseball. Tonight we've got a good match up in store between the New York Yankees and the Milwaukee Brewers. Milwaukee attempt to end a six game losing streak. Next, Brett Anderson will be on the bump for game two of the series. What do we need to know here, Danny? Here's a guy that numbers can be a little bit deceiving. He has a whip in the 1.3 area and above range. It's a little higher than league average. He's been a little bit inconsistent. One good game, one bad game, but don't let that whip for you. This guy's a much better pitcher than that. And if he brings his A game, he could be awfully tough in this one. So digging in now, DJ LeMayhew, and we are set for baseball here this evening. And the first pitch of the inning here misses down and in for a ball that's one and all. And guys, we take a look at the Brewers entering play here tonight. They are in the midst of a pretty bad stretch as they've dropped six straight coming in. Yeah, I get it, Matty. The team's on a moderate losing streak right now. Can't be happy with the way they've played, but they have to find a way to relax a little bit. Everybody goes through these little stretches, these little valleys throughout the course of a long season. This team should write itself and it needs to start today. Too far out in front that time. You can't keep it fair, two and one. And we'll see some forties before things are said and done tonight. Right now, 51 degrees at first pitch. The two-one, there's one that misses inside and the counts run full now, three and two. To be honest with you, I'm a little bit more afraid of the guy on deck than the guy that's up right now. If I'm on the mound, I want this guy up right now. He's the guy that's got to beat me. Grounded back up the middle. And that'll get on through into center field so he's got himself a leadoff single. Tip your cap if you're the pitcher right there. That was a great battle. A couple of tough pitches. Offensive player able to work himself deep into the count. Pitcher on the attack. But chalk one up for the offense on that. And that'll bring up Aaron Judge in his career against Brent Anderson. He's hitting 4-29. First pitch of the at bat on its way. And he's way off balance with the swing there. And set up behind the dish is Woody Keller as you see the rest of our umpiring crew there. You know, D-Roe, Woody Keller's a good umpire, but at times the consistency kind of wavers a little bit. I'm not sure if you'd say he's a low ball umpire or a high ball umpire. Sometimes his zone changes from game to game. Yeah, he can be a little inconsistent, Dan, no question about it, but he's approachable. As an offensive player, I just want to be able to turn around and say, is that as far as you're going today? And Woody will usually give you an answer. LeMayhew, a board here at first with nobody out. Hard hit ball to second. There's one on to first to complete the double play. Giancarlo. So striding forward now, Giancarlo Stanton. First chance for him here in the top of the first with nobody on. Infield in the over shift here, now the pitch. It was wind up. Here comes the 1-0. This is a spot you really don't want to be in with a great hitter like that. You can't just lay one in there, but you also don't want to run the count to 3-0. Timing just a tick off there as this one's fouled off to the right. Bases are empty here with two men out and he gets him to pop it up on the right side of the infield. And Jerko will make the catch here and that ends the inning. So no runs on one base hit, no errors and no one left on. Now it's the Brew Crews turn in a scoreless ball game. Jay Hap is ready to go as he'll be on the mound for the Yanks. What's your take on him, Dan? Hey, this day and age where we're all into numbers and statistics. Look at this whip. 1.10 or less. He has a sub 1.1. That's not an easy thing to do, especially in today's game where we see teams scoring a lot of runs. He doesn't walk very many guys and he doesn't give up that many hits either. This is a real good pitcher and should be fun to watch pitching this one. First pitch of the at-bat. Swing and a liner. And a base hit so he goes after the first pitch he sees and he's on to open up the inning. Now in the box, Brock Holt. And he really thrives in the batter's box here at home. Something to keep an eye on in this one. Set. Here's the nothing and nothing pitch. Dan, as the Yankees get started here tonight, guys, they've had it going the last ten games. There's seven and three over that stretch, including a win last time out. Yeah, Matt, he's taking a look at the standings right here. This team has a nice lead. Comfortable. You always want to find yourself in a position where you're about five to nine games. Got the advantage.  And this team, this team's sitting pretty well. That is good. The right field right here. And here's Christian Yelich now. No one on base for him after the double play. Yeah, Matt, that two ball really changed the complexion of this inning. It looked like the middle of the order was going to have a chance to get a big hit with some ducks on the pond. But now they just have to try and get a two-out rally started. The left field shifted well to the right. Here's the first pitch. Ball. And he runs that one high and tight for ball one. Wouldn't mind a pitcher expand in his own a little bit more and using his aggressiveness against him. Just missing here two and oh. It's a lot easier to hit when you're putting yourself in good hitters counts. This guy's done a great job not swinging at pitchers pitches. And when he's getting the ball in his own, he's getting the barrel to it. He's been hot lately. Ball. Too high. And it's three and oh. I wouldn't be surprised if he had the green light here. Matter of fact, I know he's got the green light here. He's looking for something set or cut and he's looking to do damage. And that's into the corner of foul ball and right. He got the fastball where he wanted and just pulled off of it. Here's the three one. Fastball too low and that's ball four. No left field there. So now it'll be the four hole hitters. And he's carrying a batting average of just over 300. So clearly he's been a productive player with the bat in his hand so far. There's a fastball called for a strike on the inside corner. That's a strike to throw down. Not going to get him as he swipes second. We all know this team is struggling right now. They're on a losing streak. So when that's the case, sometimes you need to be a little bit more aggressive and try to put some pressure on your opponents. Stolen bases are a good way of doing that. So we'll see if it pays off on the scoreboard for him right now. A swing and a miss as he chased with two strikes and that will retire the side. Milwaukee leaves one. We are still scoreless. Gary Sanchez. He'll get us started in the top of the second. Gary. First pitch on its way. In there at the knees strike one. Blake one ball one strike. Takes this the other way to right. Yelich is there and he has it for the out. The third base. Gio Arcella. In now Gio Arcella. He'll get to take his first cuts here. Now here's the pitch. Well below the knees laid off on the changeup there. No score here as we play in a number two. Fouled off. And the air down the right field line. But this is just going to wind up being a foul ball. Swing and a liner. A quick love at third and they were two gone. That is it. The center fielder number 11. Brett Gardner. Now at the plate Brett Gardner. And as you can tell easily from the splits he's really struggled away from their home ballpark. Ready with the first pitch here it comes. Two out nobody on strike two. You've got to go into battle mode after falling down 0-2 and find a way to work yourself back to even. This one to right field and deep off the bat of Gardner. Yelich going back and he makes a nice catch on the track as that ends the inning. One two three go the bombers. We'll go to the bottom of the second. No score. Here's the first pitch to him. And he just misses inside with the fastball there. Hap has become known as the starting pitcher that frequently works deep into games. The kind of guy you want on the staff when your team needs some rest because he tends to eat up endings all by himself. Matt every team is looking for a guy like this in a day and age where we're going to the bullpens. More early and more often you need at least one or two guys into the rotation that have the chance to get you into the seventh or eighth inning. And he's definitely one of those guys outside three and oh no. He walked a guy back in the first and now he's looking like he might hand out another free pass to the lead off guy here. You can't be walking a guy in inning and think you're going to have any success. And he takes ball for lead off man's aboard here to begin the home half of the second. Well that is definitely not the way to start an inning. One thing to give up a walk but to do it on four pitches is pretty alarming. He looks a little thrown off right now. Here's Eric Sogarn first chance for him here with the man on following the lead off walk from the stretch lifted down the line and left. Stanton will get there with ease as he puts it away for out number one. In the box now many pina he said here it comes bottom of the second here with no score. Shaved the corner with that pitch but it's one and one two and one count even a two and two working for the punch out. And the offering sliders strike three called and that's a pitcher's pitch right there to gone. He's just got great strikeout stuff in his last start. He racked up double digit base and it looks like he could finish up in that range again here. He's really an exciting pitcher to watch when he's sending guys packing like this. So it's a runner at first with two gone and up next will be the shortstop Orlando Arcea. From the belt the pitch in on the hands of it with the fastball. It's one and all as a veteran out on the mound. That's a pitch that you expect to get a call on. Got to believe he keeps pounding that spot until he builds a rapport with the umpire runs outside. So it goes to two and oh now swing and a ball line down in the left field corner. But this is foul near the seats. Now the two one pitch makes him swing and miss on a ball out of the zone for strike two.  If I'm pitching right now I'm throwing that same pitch again. That was ugly. He's set. Here's the two two heading out towards shallow right in there a base hit. Thunder will go no further than second as there are two aboard now. Nothing fires me up more than watching an offensive player stay inside a baseball drive at the other way. Brett Anderson as the first pitch to him is taken low and away for ball one. Two's all over the place two on two out and of course here in inning number two. Out off the radar screen there it's two and oh. Can't fall behind against the pitcher need to minimize pitch count against the easy outs and this is certainly one of them. The set and the two and oh two and one one one here it is. He's falling behind down three and one. Well he really needs to make this guy swing the bat right here. He's not the type of hitter you want to dance around with. Here's the three one fastball here and this is softly hit and fouled off to the left. Ready with the payoff pitch lying to the right side. A lead but he can't bring it down base hit and not in time as he just crosses the plate in time. They've had a difficult time scoring and winning any game so to strike early that RBI single right there is awfully big. Yeah. And hopefully the pitchers able to breathe the sigh relief Dan like you say all the time. Give me some early runs and let me relax and attack his own. I've always said do you score me six runs. I'm going to win a lot of games. In now is Lorenzo Kane and she'll take a change up here for strike one base hit in his first trip. A one in one count to the Brewers lead off man thirty four pitches for him through an inning in two thirds right now. That's not terrible but it's a lot higher than he'd like. Two men are on with two men out to one and two now swing and a miss got him reaching. And the throw to first ends the inning. Some of our nation's young minds and future leaders here in attendance. Yikes. The three of us returned with more Wednesday night baseball after this.  He was one for four with a double in the ballgame last night. Pitch taken several inches below the zone in fact is looked at for ball number two. And that's in there two and one unable to get the bat around in time in the count evens at two and two. Now the pitch never tempted to swing at that ball down low. It's ball three shot to second base and handled for the first down. And with that we give you a look here at what's happening in the race in the National Accentral. Stepping into the box. Look boy as he'll get his first opportunity in this one. And the pitch sinkers in there.  Two strikes on him now bases are empty. One man out. Grounder down the line at third. But this will be a foul ball and it's still 0 and 2. Nothing in two count and the pitch. And look out is that one ran in and got him. So here now is the pitcher J half. He could be bunting here in order to stay out of the double play from the stretch. Runners on first with one down. Now a bunch attempt here as he gets this one down. But that'll get foul it's 0 and 2 now. Open to send him packing pitch on its way. And did he square around. No it's ball one. While facing an AL pitcher at the plate you certainly don't want to waste too many bullets on him. I expect this next pitch to be grooved right down the middle. And he'll take no chances here as he swipes this ball away. It stays a foul ball. The runner at first here with two gone in the inning. And that'll bring up DJ LeMay here on the belt the pitch. No outside. Now this is the kind of count this guy feeds on at the plate. You can bet he's geared to hit the fastball right here. Two balls and a strike down to the Yankees leadoff man. Wow I can't believe the hitter took that one. The pitcher absolutely got away with a hanger. Not what he wanted to do there with the slider as it misses well above the zone. If you're at the plate right now you have to realize who's on deck. I guarantee you something's over the heart of the plate. You have to be aggressive in the zone right here. The three one finds the zone to fill the count three and two. Good spot for an RBI put the ball in play with the runner in motion. He could score all the way from first. This is lying to left into a slide and he makes a great catch to retire the side. The fine sliding catch here will take us to break. The three of us return with more Wednesday night baseball after this. We're back now for the Brewers third turn at bat and unfortunately for them and their fans this lineup hasn't really found its stride this season. One coach told me before the game there are certainly plenty of areas for us to improve offensively but first and foremost we need to start by putting the ball in play more often. There's too much swing and miss in our game. And the stats do back that up as they currently rank near the bottom of the league in strikeouts. So that appears to be an area of emphasis going forward guys. OK thank you Heidi ready to go for the last half of the inning at the plate. Brock Holt ready. Here's the first offering in there at the letters 0 and 1 strike on the outside part of the plate 0 and 2. He pops him up toward the left side of the infield and this is taken in for out number one. And with that we'll give you a quick look at our current standings in the AL East. Stepping up to the plate.  Here it comes just off the outside and it's 1 and 0. And now a pitch on the way. Skied in the air to straight away left. Stanton has a read on it and he makes the catch for the second out. So two away in the Brewers half of the third. And that'll bring up Abisayu Garcia. First pitch of the at bat grounded straight into the shift on the left side. And safe says a first base on fire as the throw was too late. And that's great hustle right there out of the box. Not everybody's getting it right out of the shoot from step one. But I have to ask you Dan how frustrating executing a pitch and there's an infield not. It is D-Roy and you can read that right off the bat as a pitcher. You can read the angle. You know that that ball is going to be hit on the ground and you're thinking deep down inside. OK there's a quick out and it just wasn't meant to be. And he takes ball one to out with the man at first. One in one the count of the Brewers first baseman. Hey I don't mind that batter taking that strike right there. He's walked a couple of people early in this game. We'll find out if he can find his own. If he wants to walk them all in we'll take it. Here's a bouncing ball headed to LaMahue at second throw on the Voigt takes care of him and the inning is over. Brewers strand one but they're up one to nothing. Off the inning Aaron judge and they'll need him to get something going here. Ready to deliver. Here's the first pitch hot shot on the ground is short. He has it throw to first in time one gone here in the fourth. So with one away let's punch up the graphic and show you the pitch speed comparison for the two starters here in the fourth inning. And you can see there both guys getting it up into the 90s 92 and 94 respectively and digging into the batter's box next will be Giancarlo Stanton. He popped out in his first trip runs just one hit and no errors for the Yankees so far and a sinker dips too low there into the dirt in fact he's and that's the second strike a swinging bunt out in front of the plate on the first and it's a fine start to the ending for Anderson two away now. Now batter into trying again Gary Sanchez. He's 0 for 1 thus far 50th pitch of the game on its way and this is taken outside for ball one and a strike to even the count one and one. No runs just one hit and no errors for the Yankees so far. We ground her down the first baseline but a foul ball one and two now. Now pitch on the way and this is fouled at the plate hard sinker misses two and two and good patience to hold back on the current ball in the dirt. It's full now three and two three two counts are usually a time to challenge the hitter but I think he'll be careful here shoot for the corner and if you miss and you walk him so what that's better than him putting one in the seats and awfully close but it's ball four according to Woody Keller and I'm sure the manager is just fine with that. I mean it's better to battle a slugger like that to the end and end up walking him then serving one up or he can really hurt you in Giovanni Schella is the first pitch hit out towards second and that's through for a hit and runner will go no further than second as there are two aboard now. That was a well executed pitch down and away sometimes you got to tip your hat to the offense. That's a nice piece of head and maybe not what he was looking for but the result was there. So here's the veteran Brett Gardner miss he'll watch a slider that runs out of the strike zone away for ball one two men on two away for like a slider perhaps but it missed badly and it's to an old great chance right here as a hitter to be really aggressive with two guys already on pretty good shot. He's going to get a challenge pitch right here. Two balls and a strike to count but now two and two three and two to the Yankees center fielder Torrez would be next if they can keep this ending alive off pitch on its way. Neither guy willing to give in and the ad battle continue. Now here's a ball hit high and deep is straight away right field looking up his yellow and that one is gone on a two strike count with two away in the ending. So it's a three run shot to straight away right field number eleven for him on the season and it gives the Yankees a three to one lead. Yeah he is kicking himself right now. He worked his tail off to get out of that jam and was one strike away from getting there and then boom all that work goes to waste from zero damage to a three run homer in the blink of an eye sinker to him finds the zone for strike one hit it hard but lined out in his first at bat the wind up. Here comes the O and one. Hey there's not a lot you could do with a slider breaking down and in unless you catch it way out front. I like the idea of taking it and making the pitcher bring you something a little more hittable line hard. This is a foul ball three runs already home here one to offering look like a slider that time but it's two and two the classic back foot slider right there with two strikes usually gets a ton of swing and misses nice layoff right there fight for another pitch two to doesn't get the zone count full now for the guy in the mound this is one of those innings where nothing comes easy. He's thrown a bunch of pitches and this A B hasn't been any different definitely laboring at the moment bases are empty here with two men out. This is in the air out to right. Yellow choose after it. He's not going to get it and the two out rally continues. That was a great job of driving that ball extending his arms very well was able to get it over the right fielder's head one hopping it off the wall for an easy double. That's one of those solid hits that you don't even feel coming off the bat point as the first pitch sinker misses to him. It's ball one. Hey you think the game plan is to pitch this guy inside. They plunked them in the first at that and they're clearly coming right back in again.  Now some movement out in the Milwaukee bullpen both the lefty and a right hander have begun to stretch it out. Here's the two one. Well hit but also well fouled into the seats and left. Now the two two two out here in a runner at second. This one misses and that'll fill the count here three and two with two away. He certainly has an open base down there but you don't want your defenders stand and flat footed for much longer. There's a swing and a drive hit well out to right field yell it's going back and he makes a nice catch on the track is that ends the inning. Another look at the big blow for the bombers a three run homerun bottom of the fourth coming up. It's now three to one Yanks back here in Milwaukee at Miller Park as we check in with Heidi Watney. Well not during the break I caught up with Craig Council the Brewer's skipper about his lineup's performance so far and flat out he was very pleased with the quality of their at bats. Yes they've only scored one run but he said they've done a great job of forcing the pitch count up and he thinks that's going to lead to more offense for them as this game goes on. OK thank you Heidi ready for another chance Eric so guard he flew out in his last at bat. Things not looking very good so far in this one but we're still in the middle innings down by a couple of runs and this would be the right place in the right time to get something going. The last thing they want to do is to try to come from behind and win this one in the eighth or ninth inning. The wind up and the 0 1 misses wide one ball and one strike and right into the shift but a foul ball one and two the count now. Here's the pitch third baseline but a foul ball as it holds it two and two. Now here it comes. Manny Pina waits on deck on the shoulders but it's strike three called and a questionable first out of the inning. Well it's still early but it's also worth noting that he'd be in line for the win if this keeps up as we take a look at the league leaders in games one this season and as you can see there he's part of a flat footed tie for the A.L. lead. Stepping into the box Manny Pina hold for one for him here in this one. He's ready. Here's the first offering. That's a great take right there. Backdoor slider just missed the outside corner. This guy must have a really good eye. Most guys swing at that pitch. No offer on that one two balls and a strike. Pretty well struck high and deep to left field. Back goes Stanton. Boom goes the dynamite. Polo shot here to left his first home run of the season and the group crew has got this to a three to two ball game now. Now one right now and feeling pretty good they can come back or see it. No watch one miss up and away for a ball. One and only misses two and all. One half nobody on a good comeback fastball there.  The two one pitch. He stays alive still two and two. Another foul ball to two one more time. Hit down the line at first and he'll take it to the bag himself for the out. Now that the pitcher next to it'll be the pitcher Brett Anderson. He singled his last time up. Yeah he showed like a little prowess with the bat right there Dan. I'd be surprised if they don't attack him a little bit more carefully this baby first pitch hack in here and that's the first strike two out nobody on he looks like he's toying with him here. It's 0 and 2. Hey this guy obviously feels he can move traffic right here. He's taking two big swings he's trying to help himself one and two to the Brewers pitcher hit to first the Brewers get one back on the soul ball home run. We're through four it's the Yankees three and the Brewers two. So now the pitcher for the Yankees Jay Hap and Dan I'm sure the starter on the mound would like to hit the rewind button on that last inning. He's still got about that Mac that was a really rocky frame but clearly not enough to chase him from this game. We'll see if he's still shaking a bit or if he's able to put this behind it. Ready with the first pitch here it comes high fly ball out to straight away center after it is Kane. He gets there and makes the play for the first out. Now that second base. So it's back to the top of the mound to bring in DJ LaMahieu first pitch on its way and looked inside but that's ruled to strike nothing in one. Great job by the pitcher right there. Change in eye levels. We all know he's a sinker ball pitcher but if he could throw some four seamers up in his own like that it could work for him. Throw on the first two gone Aaron. So bases are empty here with two gone and that'll bring in league rookie of the year. Big Aaron judge. First delivery to him on the way. Fifth inning a play here in a three to ballgame. Two and oh now two outs nobody on but a base runner here feels like it would really change the complexion of the inning big spot right here. Middle of the order guys coming up and see if he can extend the inning and here's a slider for a cold strike nasty two oh slider right there for a strike. No shame in tipping your hat. Sinker misses there and now he's in trouble three and one. This is good patience here to work at the three and one especially after two quick outs to start the inning. Even if you don't end up getting a hit or drawing a walk at least you're making the guy work a little bit and giving your pitcher a chance to rest a little full count three and two. The miss for the third strike as he went after what would have been ball four instead the inning is over. So the Yanks go one two three and it remains a three to two ball game. And in the hit next is Lorenzo Kane and then he and his fellow top of the order hitters haven't really offered much help for this lineup so far. No you're one two three guys are the ones you look to to generate a lot of action and they just haven't been up to the task so far on this one still time for them to turn it around though. We'll see if it happens. Here comes the first pitch check to swing there and pops this one up. The Mayhew has it and it's a quick out number one the batter. So the bases are empty with one man gone and that'll bring up the versatile utility man Brock Holt. He's ready. Here's the first offering in there. Oh and one. Boy that's just about in the catchers glove there.  Well he's really locked in at this point in the game on the bump. So far this inning four pitches and two outs got the first guy on one pitch then absolutely dominates this at that with a three pitch strikeout in his Christian Yellich as he will take a fastball in there at the knees for strike one Yellich could be making an appearance at the Midsummer Classic this year. So far he's received the second most votes in National League right fielder balloting. Yeah and he's been having an excellent season to date making a push towards that all star game.  This guy sits in second place but I'm sure he'd like to be named starter from the wind up the one one pitch not surprisingly here this is on the ground to the right side go to first to get him easily and the side is retired gone in order of the Brewers they trail three to two David Phelps takes over to start the sixth inning on the mound number forty one. Giancarlo Stanton now over to the left side of the mound and the left side of the mound is lined this far ready to deliver. Here's the first pitch and who looks like he got the call there on the pitch inside it's nothing in one off the plate one ball one strike one and two. Now is that one's fouled off here's the pitch and right into the shift. But this is a foul ball as the left side of the mound got to take advantage of that pitch right there.  Now this guy's a grinder fouls off good pitches and doesn't seem to swing at the ones just off the corner. This guy's a pitcher's nightmare sent on the ground but right into the shift throw to first gets him so the lead off man's retired now better. Gary ready for another shot now Gary Sanchez first offering on its way action now with the Milwaukee bullpen as they'll have a right hander loosen up the wind up and the 01 and one and one is this one's in on the hands one and two to the Yankees catcher three twos are scored here and ending number six to two balls and two strikes now and deep to right center yell at John the moon and he tracks it down a nice running play to record the second out. Digging in and looking for more Geo or Shella a hit in two tries so far hit on the ground toward the left and there's a base hit as that gets through into left so it's a ground ball single to left for him here his second hit tonight and as that graphic shows us he currently leads the Yankees in that category was tried in again as first we flash it back to his at bat in the fourth inning and what a big one it was a three run homerun that was certainly one of the big blows in the ball game to this point from the stretch. Here's the pitch lifted the other way down the left field line and this will wind up a foul ball the 01 pitch and there's a fastball well off the plate inside strike two is the fastball that's let go a bouncer up the middle or see a gloves it and an underhanded throw is in time for out number three Yankees leave one but they still lead it three to two. So here's obviously Garcia a hidden two tries for him so far here comes the pitch for Garcia and up here comes the 1 0 and right into the shift a quick out number one coming to the plate now Jed Jericho he was retired via the ground ball last time up first pitch on its way now a swing and he pops him up. This is right out in front of the mound half with a little do it yourself play and there are two down so yet another strong out in form tonight as we show you the league leaders in ERA and as you can see he currently ranks second in the A.L. in that department standing in Eric Sogard he's 0 for 2 thus far in this one ready with the first pitch here it comes I left a high pop up drifting into foul territory on the right side and this will not be caught it's a foul ball. Now the one in one pitch is taken for ball to big sweeping breaking ball right there a good pitch but if he wants to get him to swing at it he'll have to bring it in a little bit closer to the strike zone bases are empty here with two men out in the air to right center and carrying well way back there now and gone home run for him on the season and the Brewers have gone even now with three three normally this matchup is the last thing you want to see left on left but he kept his front shoulder square stayed in that at bat and absolutely demolished that baseball any Kenya as he looks at a fastball that's in there for strike one one for two in the ballgame thus far for the wind up here comes the 0 and 1 two out nobody on protecting on 0 and 2 so we'll do it again trying to send them packing for the second time hard on the ground towards short dive and he knocks it down and the recovery will not be in time at first and the ending will continue following the infield single nice effort by the short stop right there kept it in front of him that's that's all he could do right there Dan you know dealer in a spot like that that's an infield single that's a tough play just to knock that ball down was a pretty good job but any way you look at it that should be scored a base hit and I'm sure it was stepping in now Orlando Arcia no balls in one strike well above the letters with the fastball that time double barreled action in the Yankee bullpen now a lefty and a right-hander start to get loose a runner on first with two away lays off the slider that time two and one the knees for a called strike and it's back to even at two and two from the stretch three to two out runner on first lots of possible outcomes on this pitch ready now with the pay off pitch rounded down the third base lot but this will get foul so they'll do it again three and two hit the other way out toward right field heading after his judge he's there to track it down and that'll end the inning but the Brewers tie things up thanks to this solo home run bottom third of the order seven eight nine do up to start the seventh we're tied now with three apiece Ray Black is on to pitch from the bullpen now to start ending number seven number picking stepping up now Torres he doubled his last time through and he's got to build off that last day he battled usually when you battle you get in that swing mode a lot of pitches you'll swing at the rosin bag I love the fact that he was able to work a double in last at bat let's see if we get more of the same right here down the left field line and deep and that will end up a foul ball 0 and 1 here it comes popped him up Kenya shading to his right and that's the first out of the inning now that that's exactly what they wanted out of that pitch up of the zone they took him up the ladder and he couldn't get up to it so that was an easy pop out well executed pitch there digging in once again look white it was a flyout for him in his last trip first pitch on its way bases are empty one man and that misses low on inside two balls and no strikes and not the kind of swing you're hoping for on two and oh as they bunch him up inside it's going one now not much you could do with that one tied him up in knots now the two one is looked at for ball three every base runner in a close game like this really matters so you can't afford to be giving out free passes this late three ball now the three and two picks and he lays off ball four now the potential go ahead run is on base here Miguel Andujar come on to pinch hit here in a big spot I strike called there that's not all that consistent but it's strike one the winner play here at an even two fifty five homers and twenty two RBI up the middle fielded by so guard on the first as they get the double play to get him out of the inning so they breeze through this half of the inning seventh inning ballpark and we are all tied at three a piece Tommy Keenley gets the call from the pen to take over on the mound and start the home seventh Boston here up off the bench as he'll be asked to get something started in the home half of the seventh first pitch fastball in on the fists for ball one ready with the one oh pitch swing and a ball lifted in the air toward the line and right judges under it and that's the first out of the inning away for the Brewers in their half of the seventh and that'll bring up Lorenzo Kane and the pitch and he takes a cold strike oh and one in going to miss here and he's behind in the count now oh and two one out nobody on hit the other way out toward right field judge is there two down up next to the walk the third baseman here's Brock Holt now the liver here's the first pitch Keenley 30 years of age he was a first round pick back in the draft of 2013 yeah Maddie they certainly got it right when they drafted this guy he has turned himself into an absolute superstar everybody knows this guy's name and kids are buying his jerseys two balls and no strikes sometimes it can be difficult for a pitcher you're facing a guy that's not known to be a big stick in the lineup sometimes the toughest thing is to be aggressive and throw strikes popped up Burcella is there for it and that retires the side three up three down for Milwaukee still tied three to three Brent Souter will come on to make his 40th appearance this season and that sends D.J. LeMahieu into the box he was a ground out victim last time up pitch on the way a one and no delivery and this is low ball two two and one tough to lay off a breaking ball that good but he saw it all the way popped him up Jerko in foul ground and then he got to give you a look at our starter comparison in this three three ballgame both pitchers turning in fairly good performances as you can see on the graphic here's big Aaron judge is the first pitch to him lays off one and oh action in that Milwaukee bullpen now as a left-hander started to throw out there and a strike to even the count and now he's going to throw it out to the left hander. Now here's the pitch swaying and a miss on the fastball and it's one and two that's not a pitch he misses very often he knows he should have done something with that one and he lays off a pitch outside as they draw even at two and two well I'll tell you he's not hitting over three hundred by luck he really knows the strike zone and his own strengths that last take is a great example and this pitch is swung on and missed in the A.L.'s leading hitter is set down on strikes two away anytime a pitcher locates a fastball on the inside corner it's going to be a tough pitch to hit that one was spot on and he had no answer for it into the box now Jean Crello Stanton as he takes a cold strike at the knees its own one we could really use a knock here 0 for three in the game so far and it's a ball and a strike I know we buried that slider in right there but that's a dangerous pitch if he doesn't pop commit and bury that inside it leaks out over the plate he can get hurt with that pitch Jean Carlos swings and this ball is hit well into that field but he will make the catch on the dead run as he tracks it down just shy of the wall and the side is retired one two three go to bombers no change in the score it's three to three Ben Heller is on the pitch out of the bullpen in the bottom half of the eight digging in Christian Yelich he'll get things started now in the bottom of any number eight here comes the first pitch just misses off the inside for ball one spins on one here and drives it to deep right there in the field and he's going to have room to put this one away and that's the first out next will be the clean up hitter of Issaiel Garcia he's working on a one for three thus far and the pitch hanging a miss on the slider nothing in one and some action out in the Yankee bullpen now as a right hander starts to loosen the ball one man out and a sliders in the dirt as he lays off it for a ball of the one and one pitch lifted down the line and left and this is going to get down it's a foul ball trying to get him fishing there but he won't offer in the dirt and it's back to even a two and two fighter good patients and it's full three and two fighter in there for a called third strike and there are two gone now that was a big strike out there guys have the ability to strike guys out when they really need to and that second out was really important at this point in the game could be something we look back on later when the game's over here's Jed Jerko now as he will look at a first pitch fastball for ball one he's hit listen is to add bats so far all in a strike bases are empty here with two men out now come back with one in the third as the count moves to two and one now he misses good breaking ball there laid off for the second strike ball had fouled down the line and right and in amongst the fans here's the payoff pitch popped him up Sanchez is there and that's the third out gone in order of the Brewers score remains tied at three to three winning set to get underway digging in Gary Sanchez over here ready with the first pitch here it comes a great job pounding his own strike one when you got a great hitter in the box got to get ahead count leverages a must it's 0 and 2 to Sanchez after falling down 0 2 on the same pitch don't be shocked if he triples up on it cold take right there that fastball very well could have sent him packing back to the bench easy take there is the off speed pitch misses well inside the pitch swung on and bounced to Arsia it's short on the first and that is a big out to start denying your shell up two hits in three at bats for him in this one ready to deliver here's the first pitch not close with that when it's way above the strike zone it looks like this guy's going to work in the upper part of the strike zone will be interesting to see if this lineup can adjust to the way he pitches is in there for the strike 1 2 down the left field line and deep and no one will get this one the 1 2 1 out nobody on fastball blew it right by him and there are two down well there's nothing better from a pitcher standpoint to watch in that high fastball a high piece of cheese swung at a miss that pitch looks so inviting to hit but it's awfully tough to put in play Brett Gartner now first pitch swing he hits a fly ball to left center hold he's got it and the side is retired so the Yanks go 1 2 3 still tied 3 to 3 Roy this Chapman enters the game from the pen and because this is a non safe situation it's evident that they're just trying to get him some work after having not thrown in several days yeah and this is all about just getting him some work guys he hasn't a chance to come in and close the game out for several days now so they're just hoping they could keep him sharp and give him a chance to pitch in a real game situation here one ball no strikes to count and it's fouled away one and one pitch is taken for strike two like a slider that time but it's two and two struck him out second time tonight now that he's been set down on strikes into the box many Pena he homered earlier in his two for three to this point first offering on its way I got him fishing that time 0 and 1 you got to be paying attention as you're in offense in a hitters meeting in this situation when you've got a guy on the mound that you know the bottom can drop out of any pitch he throws you have to elevate your sights faces are empty one man fouled away the 0 and 2 and he strikes him out as well so make it back to back punch outs here to the first two men he faces out of the bullpen no problems for him on the mountain since he's come out of the pen to start this sitting that's back to back he's making it look pretty easy this has the makings of a good outing so far at the plate Orlando Arcia as he'll look at a fastball in there on the outer half it's 0 and 1 Chapman neck named the missile for obvious reasons he's an 11 year vet at the major league level so he certainly puts together a nice career in professional baseball come set the 0 1 big swing and a miss at the fastball and he's behind in account 0 and 2 in my opinion there is no one in this bullpen that relishes a moment like this on the mound other than this guy it looks like he feeds off the challenge of pitching in tight games a swing and a miss at a sinker the strike out retires the side inning is over three up three down from Milwaukee no change in the score it's three to three digging in now for the Yankees Torres his last at bat didn't know his way as he popped out in foul territory yeah we used to have a saying right here you would try to the ball here's a five ball well hit looking up his yellow and his Yankees fans here on television quite frequently see a solo shot here to straight away right field as they take the lead four to three that we've now seen four homers combined between these two clubs today what are your thoughts guys yeah man one of the things you look for when you come to a Brewers game at Miller Park you want to see Bernie Brewer go down the slide and Bernie Brewer's fan he's got to be a little bit sore after this one damn one of my favorite places to do that I always felt like great batter's eye and dead center you can move traffic to both gaps a lot of home runs get hit in this yard comes into this at bat 0 for one in the ball game ball and a strike I changed things up on him and he got him to swing through it one and two now off the curve ball that's in the dirt that time and it's back to even now at two and two looks like that bomb earlier in the inning kind of put this pitcher on the defensive being very aggressive right now three and two full count the payoff pitch home and awfully close but it's ball four according to Woody Keller just a nice piece of hitting right there especially in extra innings he didn't try to win the thing by himself for be a hero he just patiently worked the bat until he earned the walk we'll see if his teammates can pick him up now my talk man will grab a bat and hit for the pitcher here he popped him up Garcia coming on but this will land untouched here comes the 0 1 swing and a miss and he needs a little discipline here 0 and 2 it's not easy to get your barrel to a pitch that high that could be an effective location as long as he keeps it above the letters hurt and now let's see and it's not in time as he's in well ahead of the throw and that's going to move that runner into scoring position now well I know what he was thinking there the pitch before was way out of the zone and he was hacking so the pitcher says hey if he's going to swing at that how about this solid strategy except this time it didn't work out and it's a wild pitch he lays off it to even the count two and two he went with the all speed there once he got him the 0 and 2 but now that they both missed I think we'll see more of a challenge pitch here you don't have to give in but you can't be too cute either and that would never threaten the zone it's gone full now to three and two that was kind of a gift to the hitter he's up there probably thinking of protecting on two and two but when you launch a ball that high out of the strike zone it's obviously easy to take that one working for the punch out and the offering swing and a miss on the slider and that's out number one well his struggles continue it's been a rough goal that at the plate with him and watching this at bat it's clear to me that his rhythm and timing they're just all off even as a pitcher like I was you can tell these things and exploit them here's the second baseman DJ LeMay here as he'll take a look at an off speed pitch here that misses for ball one he comes into this appearance in the midst of a one for four day of a fast ball here that looked pretty good but it's two and oh that's a tough call for blue right there either way you call it somebody doesn't like it but hey that's the life of an umpire too well count the pitch is a breaking ball that's taken for a ball Aaron judge waits on deck that misses ball four so it's first and second now with only one away it was obvious when the count ran the two and oh that they were not going to give this guy anything to hit sometimes you have to pick your battles and they're going to try their luck with the next hitter first pitch on its way a swing and a drive to center field that one's got a chance Kane going back and off the batter's eye for a home run an impressive shot to dead center field so a three run blast to deep center here number 14 on the season as it is now seven to three Explodio will come on now to make his 30th appearance of the year so far number 58 John Crello stand as the change up to him drops in there for the first try Claudio has seen his role change with those one batter lefty specialists going the way of the dodo is a part of MLB's pace of play initiatives and he misses with it one and one player misses that time and it's two and one that's where he wants that sinker to end up but that was a nice job of laying off four runs here in this half inning and not an easy pitch to lay off of but he did somehow and he's got it to three and one good job to work to count and put himself back in the driver's seat started off with one strike and now he's got to count his favorite three and one and he misses ball four so he comes out of the bullpen and immediately walks the first man he faces and you can tell by his body language that he's beyond frustrated by that call he's got to be wondering what he's got to do but the last thing he needs to do is to let it get under his skin that will only make things worse now batting Gary Sanchez he got on top of one it was a ground out victim last time first pitch of the at bat on its way and that's in there for strike one still only one out in the inning rounded weekly down the line toward third but this will be a foul ball as his behind Owen to now nothing in two count and the pitch skied into straight away right after it is yellow he gets there and makes the play for the second out of the inning and this throw gets away from him coming to the plate now Geo or Shella he looked to bounce back after striking out his last time up ready to deliver here's the first pitch he won a home is taken strike one two out with the man at first while they have him looking awfully confused up there right now it's one and two man this guy's been locked in all game long I don't know where that ugly swing just came from the one to changes up on him if that's in the dirt for a ball sent on the ground out to second on the first will finally retire him as the inning will draw to a close so four runs in the inning and they come on the strength of the two big flies so now we'll see if these guys can get even in the bottom of ending number 10 it's the Yankees seven and the Brewers three. You're a Britain of South Boston in six foot three gets the ball now out of the bullpen. Ben Gamble is up off the bench as he'll lead off the bottom of the 10th after a disastrous top of the pitches taken on the inner half for strike one Britain a California born ball player this is his tenth season at the Major League level so almost a decade which is quite an accomplishment barely able to make contact down 0 and 2 now nothing in two count and the pitch it's one and two Gamble is usually more of a threat when facing left handers like this the right handers tend to give them a bit more trouble so we'll see if that trend continues and a slider runs away from him there and the count levels at two and two here's the pitch and he takes ball three so it's a full count now from 0 and 2 to 3 and 2 what a great at bat to start this inning off. Hey this could be a productive inning off pitch home popped up and the pinch hitter is retired here one away the center fielder now back to the top of the Milwaukee order digging in Lorenzo Kane.  Here it comes. He'll start him with a sinker here but that sinks a bit too much that time. It's one and oh two and oh to the Brewer center fielder I'm seeing him just a little to amp up out there right now that's common with hard throwers like him running a blazing fastball up there is great but if you can't harness it what good is it do you. One out nobody on all three laid off but in there for strike one three one lifted in the air out towards left center under it now is Stanton to make the catch and there are two away now. Now batting the third base training. Striding into the box Brock Ofer four with a strikeout this far. Britain's ready. Here comes the first pitch. And that misses ball one two and oh Woody Keller's just not giving him any help now. It's three and oh Christian Yelich would be next if they can keep this ending alive three oh and that one's taken outside for a ball we walked him so no one two three ending here they've got themselves a two out base runner. That is just a great at bat there when you're down late you need base runners any way you can get them and that never say die mentality could be the difference we'll see how it plays out. Striding in Christian Yelich and we'll see if they can make him pay for the two out walk always considered a big no no of course from the stretch no pitch on the way well this is spot you'd like to be in two oh good hitter he's going to turn it loose right here and that one's wide to the mark ball three of Issaiel Garcia would be next here it is the three oh swing in a miss that's the first strike that swing had one purpose and that was to put the ball over the wall. I guess he doesn't have much to lose with his team down this many at this point in the game three one and he misses again ball four and that's back to back guys now the ball's going to go through the two outs via the base on ball. Oh man I think this walk is going to grind him for a bit he just missed and now the inning continues with the man in scoring position. So striding in Issaiel Garcia he got called out on strikes his last time through. Yeah always frustrating to go down looking everybody does it though you'll have a few A.B. is where you get completely fooled. Look for him to be on the attack early in the setback a splitter but he started up one and one looking to wiggle out of this. Here it is. Now a swing and he pops him up and this should do it and he will make the catch with ease and the Yankees have taken the first two games of this series on the road as this one is over. Hey it took him an extra frame to do it. But hey they're not going to fight as they lock up a nice road victory here in 10 innings and tonight's final seven to three a road this Chapman claims the win out of the pen his first. So that's a wrap here tonight for Mark DeRosa Dan please act in Heidi Watney. This is Matt Vaskersen. You've been watching MLB the show for more. Find us on Twitter at MLB the show.


In previous lecture, we derived equation of motion and that equation of motion was derived with reference to descent trajectory means how the particles are travelling at a displacement with respect to descent trajectory and what the trajectory of these particles are making an angle with respect to descent trajectory. In this manner, we derived equation of motion and that equation of motion was under the dipolar magnetic field and quarter polar magnetic field. Dipolar magnetic field means a constant magnetic field over a space and quarter polar magnetic field means magnetic field has some gradient over the space. Under these magnetic field configuration, we obtain the equation of motion that is the second order differential equation. Now we will solve it by one of the methods known as matrix method. This is a very powerful method which provides a tool to calculate the trajectory of particles from each of the magnetic elements. So trajectory from entire optics can be computed using this matrix method. So in this lecture, we will see this. Now this is the equation of motion in the horizontal plane and this is the equation of motion in the vertical plane. Here you can see these equations is much more like the equation of simple harmonic oscillator. However, there are certain differences. What are those differences which we will see here? Here in this equation kx is basically 1 by rho square plus gradient of the magnetic field normalized by magnetic rigidity. Normalization by magnetic rigidity actually makes our calculation energy independent. So everywhere in accelerator physics, you will see that formulation have been normalized by the magnetic rigidity. Similarly, in the vertical plane, we have ky, the gradient in the magnetic field normalized by the magnetic rigidity, however, there is a minus sign means gradient in the horizontal plane has the positive effect than the vertical plane. So in horizontal plane, if gradient is providing a focusing, then in vertical plane, this gradient will provide the de-focusing, which we have seen during the study of the quadrupole magnet. And in horizontal plane, you will see an additional term of 1 by rho square. Why this is an additional term? Because we assume that the bending is taking place in horizontal plane means we are making our accelerator in which design trajectory is completely in the horizontal plane. So this is our assumption and we are under this assumption, this 1 by rho square appears only in the horizontal equation of motion. So now, we will solve this equation of motion using some method. Using accelerators, we use different kind of magnets for different purposes. Now, you have learnt that the dipole magnet is used to decide the design trajectory, how much curvature we have to produce, where we have to send the beam and that design orbit is decided by the arrangement of dipole magnets. So the dipole magnets basically decides the design trajectory. So we can say in accelerators, dipole magnets, this design decides the design path or trajectory or orbit. And what the quadrupole magnet does, quadrupole magnet does the confinement of the beam around this design trajectory which is decided by the dipole magnets. So quadrupole magnet is used for focusing of the charged particles and each of these magnets, if we are assuming pure dipole magnet, pure dipole magnet means the constant. And quadrupole magnet, it means it has only gradient part in the magnetic field, means it has G which is del P y by del x. So these magnets have different K in the equation of motion. So in the equation of motion for the dipole magnet, if this is pure dipole magnet, means without any gradient, then we will not have any gradient related part in the K for the dipole magnet. And if it is a pure quadrupole magnet, then we will not have any curvature related part in the equation of motion. So each of these magnets have their own value of K. So for each of these magnets, we have different equation of motion means we have different K and we have different equation of motion. So again we see, now first the simplest structure in accelerator is the drift space. Drift space means a vacuum chamber connecting a straight, connecting two magnets or two points with a straight line means there is no magnetic field over this region and particle goes straight without feeling any force. So any trajectory which is going, it will go on its course in the drift space. Means drift space has no K. So in drift space in horizontal plane and in vertical plane, in both the cases we have K x and K y 0. So for the drift space, we have very simple equation of motion that is d 2 x by d s square is 0. And similarly d 2 y by d s square is also 0. This is basically a differential equation showing the straight line. In the dipole magnet, as we already discussed that curvature related part will be there. So in dipole magnet in the horizontal plane, we have K is equal to 1 by rho square plus gradient related part. However, we are considering pure dipole magnet means no gradient. So K x will consist of only 1 by rho 0 square. So K x is equal to only 1 by rho 0 square. Now in the vertical plane, in a dipole magnet, there is only contribution from the gradient part in the K and as we are assuming that no gradient is present in the dipole magnet, so K y will be 0 in this pure dipole magnetic field. Now in the quadrupole magnet, curvature related part will be 0. So only gradient related part will be in the K x and in K y also only gradient related part will be there. However, these gradient are opposite to each other in sign in the equation of motion. And in the last, a combination of dipole and quadrupole may occur, which we have seen in our course of weak focusing that if dipole magnet has some gradient, it can produce a curvature as well as focusing. So this type of magnet, which is a dipole with some gradient is known as synchrotron magnet. In this kind of magnet, we have curvature as well as gradient effect both. So K x will consist of curvature part as well as gradient part, this is the case and in K y, we already have only gradient part. Now again here, you can see by introducing the gradient, actually we are introducing the quadropolar component in the magnetic field. So if gradient part is producing some positive effect in the horizontal plane, it will produce some negative effect in the vertical plane. Sometimes if gradient is introduced in such a way that if it is producing focusing effect in the horizontal plane, then it will produce the defocusing effect in the vertical plane and vice versa. Now in accelerator, even a simple optics, we have a regiment of some magnets. And we can see that in actual optics of charged particles, we can have some quadrupole, suppose this is a quadrupole Q, then some drift space and then again there may be a dipole magnet which bends the trajectory in the desired way. So this is a dipole magnet. And then there may be again a drift space means no magnetic element, then again a quadrupole and like this. So now if we consider here the value of K in our equation of motion, you can see that this quadrupole, you can see this is the quadrupole 1. So it has its own K value Kx which depends on the gradient of this quadrupole magnet. Then this is the drift space, here you will have K2 you can say this is 0, then a dipole magnet, it will have its own K in the pure dipolar field, it will have only curvature effect in this K and in vertical plane, the K will be 0 for such kind of magnet, then again you can say this is a K3, then again a drift space. So you can say again K4 which is again 0 and another quadrupole you can say this quadrupole is Q2, this may have the strength different from the K1, so it may have its own strength K5 and like this and this optic axis in our coordinate system is designated by S. So we can see that the K varies over S, when K varies over S actual or a differential equation we can write explicitly in this manner where K is shown as a function of S means K is a function of S and this is the striking difference of this equation with that of the equation of simple harmonic oscillator. In simple harmonic oscillator we have d2x by dt square plus omega square x is equal to 0. Here omega square is a constant for a given oscillator, here you can say this is not a constant instead it depends on the independent parameter S. So how we can solve this equation? In this class we will see that we can break KS or KS function of S in the pieces where we can make this K independent to S and then we can solve the equation. How we can do this? We see now. Suppose there is a quadrupole magnet and then there is a drift and there is another you can say dipole magnet or like that quadrupole then drift and then dipole magnet. Now as we have said that this has its own K value. So within this quadrupole length you can say we have K as a constant. After this quadrupole K becomes 0 but within the drift space length this is again constant quantity K is equal to 0. Then in dipole if dipole is of sector type magnet and there is no gradient then it has certain K decided by its radius of curvature. Again within the body of this magnet this K will be constant. So within each magnet K has its constant value so within each magnet our equation will be exactly similar to the equation of simple harmonic oscillator and when in a single magnet we have equation like the simple harmonic oscillator. So we can write down easily the solution of this simple harmonic oscillator equation as we know that XS is equal to A cos root KS plus B sin root KS and these A and B can be decided by initial conditions. So this will be the solution of equation of motion when we consider as constant K inside a single magnet. It is derivative because we are going to solve second order differential equation so we need two initial conditions. So first initial condition can be the position itself and the second initial condition will be the derivative of this X prime which shows the angle. X prime is dx by dS and it represents the angle in the perexial approximation as we have seen. So differentiation of this quantity will give you root K sin root KS with minus sign which is written here and root K cos root KS which is written here. So this is the derivative of the first equation which will be the X prime. Now at the initial point, initial point we can consider as the beginning point of the magnet and at the beginning point you can say S is equal to S0. It is the our beginning point when the particle enters inside the magnet and starts feeling the force designated by this K. So at that location we can have at the beginning X is equal to X0 and X prime is equal to X0 prime. These are our initial conditions at S is equal to S0 at the beginning of the magnet. So we can put X0 value in this equation so we will get X0 is equal to A cos root KS0 plus d sin root KS0 and similarly we can put X0 prime in this equation so we will get X prime 0 is equal to minus A root K sin root KS0 plus b root K cos root KS0. Here now because we are solving a given magnet equation of motion in the given magnet so root K is known to us. S0 is the initial point of the magnet from where the we want to solve the from where our particle will trace out its path inside the magnet. So this is the starting point of particle trajectory in the magnet X0 and X0 prime these are initial condition which we know. So now in these two equations there are two unknowns one is A and another is B. So we have two equations two variables we can solve it very easily. So solution will give you A as a function of initial conditions X0 cos root KS minus X0 prime root K sin root KS0 and similarly we will get the B and B is equal to X0 sin root KS0 plus X0 prime root cos root KS0. So now we have A and B as a function of initial condition. So if we put these A and B value in our solution we will get the particular solution of that differential equation. This solution was the general solution equation of the differential equation and now when we have particular value of the A and B and we put these value of A and B in this equation we will get the particular solution of that differential equation. So let us obtain that particular solution. So at the place of A we have written the value from the equation 274A this is A and you now know A cos root KS and this is the value of B so this is B sin root KS. So in our solution of differential equation we have inserted the values of A and B in the form of initial condition. So now this X is as a function of initial condition and magnetic strength K here in this equation. Similarly we will get X prime also. Here you can see this is the again A and this is the value of the B. So now what we can do? We can collect the term of X0 together. So you will get X0 and inside bracket you will get cos root KS0 cos root KS plus sin root KS0 sin root KS means you will get X0 cos root KS minus S0. Similarly when we will collect a term containing X0 prime you will get such kind of trigonometrics formulation there also similarly for the X prime. So finally what we will get? We will get X X0 cos root KS minus S0 plus X0 prime root K sin root KSS minus S0. This is our final solution means X at S as a function of initial coordinates X0 X0 prime and magnetic strength K. Now if this S suppose this S, S0 is our beginning point of the magnet. If S is at the end point of the magnet then this S minus S0 is actually the effective length of the magnet and in that condition these X and X prime will be the coordinate of the particle trajectory at the end of the magnet. So we have obtained the coordinates of the particle trajectory which is passing through the magnet if we know the initial coordinates means if we know initial state of the motion of the particle we get the final state of the motion of that particle using these solutions. So now you can see from here this we can write down X is equal to X0 and some term related with cos plus X0 prime and some term related with sin and similarly X prime is equal to X0 with some term related with sin you can say 2 and plus X0 prime with some related to 0. So these solution can be written down in the matrix form which is written here and the element of the matrix are cos root kl 1 upon root k sin root kl and minus root k sin root kl and cos root kl. Here you can see that the second row of this matrix is basically the differentiation of the first row and this should be because we have X and X prime X prime is the differentiation of the X. So second row should be the differentiation of the first row and in this manner if we know the initial coordinates of the particle we can get the final coordinates. Here this solution is most general. Most general means we have obtained the solution in terms of k and we have seen that for different magnets k has different values for dipole magnet it has 1 by rho square for quadrupole magnet it is just the gradient normalized by the magnetic rigidity and in the case of drift space k is 0. So if we will put these particular values in this matrix we will get the matrix of that particular magnet. So we will obtain now matrices particularly for drift space quadrupole magnet dipole magnet and one another type of magnet which is known as wage magnet. What is that wage magnet? We will come to that point.