I got to admit that whenever myself and some of the other former fire staff here at Bandolier were asked to do a presentation as part of this staff ride, we had some real mixed feelings. On one hand, we were being asked to open the book to the perhaps darkest chapter in our lives, and that's kind of a hard thing to do. But on the other hand, we were really motivated by the fact that if our presentations could keep people money, you guys, from having to go down the road that we did and deal with everything that we dealt in the aftermath of Serial Grande, it would be more than worthwhile. Welcome to station one of the staff ride. I really hope you have a very productive learning experience. The staff ride is sort of set up like chapters of a book. And this station one is the introductory chapter. And what I'm going to try to do here is this set the scene and the context for the Serial Grande prescribed fire. I want to talk about a couple of previous significant fire events that sort of shaped the thinking in this area. Talk about the overview of the interagency setting and the park organization. Discuss a few key aspects of the fire management plan and other activities that occurred during the fall, winter, or spring prior to the Serial Grande prescribed fire. And the first prescribed fire that was conducted at Bandolier was in the fall of 1978, that was a year after the La Mesa fire.  And in fact, the first large fire that spread onto the lab threatened the laboratory facilities in the town of Los Alamos. That was a human caused fire that was started on June 16th, 1977. And if you look out across here, if you look at the burn scars on those maces, that was the La Mesa fire. Came from the west to the east, blew across here, blew across the park. When it entered the laboratory, and it was just a stroke of good fortune that no laboratory facilities were burned during that episode. I was told that that fire was the first time that ICS was used in the southwest of the 1977. So that's kind of one of the things that made it significant. And what is interesting about that is that even though it spread onto the lab, threatened facilities, for whatever reason, it didn't serve as a wake up call to the land management agencies, to the laboratory or the community that you know were at risk here. Not really sure why that is and talking with some of the old timers.  And it just seemed to pass from people's minds. Let's fast forward to 1996 in the dome fire with the second large fire that Bandolier experienced. And that was another human cost start, started on Santa Fe National Forest land, spread onto the park and had great potential to enter Upper for Holies Canyon, run through that, and threaten the laboratory and the town site. And it was only the success of a pretty dicey burnout operation that prevented that from happening. The 1996 dome fire was a significant wake up call. Folks recognize at this point that you know there's something wrong with this picture, we do have a fuels problem, the laboratory is vulnerable, the town site is vulnerable, and we have to do something about that. There was also some recollections back to the 78 La Mesa fire that going boy, that burned kind of similar to the dome fire. This has happened more than once. We're not going to continue to be lucky. And then during the time period between 1996 to dome fire in 2000, Bandolier conducted 10 prescribed fire projects, totaling nearly 6,000 acres. The primary focus of those projects were improving the defensibility of the park and lab boundary and to reducing hazardous fuels around some of the key park facilities, residential areas, campgrounds, visitor centers, those types of things. A significant driver of the parks fire management program was data from extensive fire history study that was done throughout the Hamas Mountains. Tom Sweatendom, Craig Allen, and a number of others were involved in that. And basically what the fire return was, but pre 1900, the mean fire return interval range from five to 25 years throughout the Hamas Mountains. Genity that shorter return interval was associated with lower to mid elevation ponderosa pine and the longer return interval was a higher elevation mix conifer. And then the fire history basically ended in 1890. They couldn't really find any fire scars after that time period. This is initially due to some changing land use patterns, i.e. a whole lot of sheep grazing during that 1890s, early 1900s. And then as it evolved, then fire suppression also had its hand in ending that fire record. As we got into the early mid 90s, they were doing a better job of looking at the fire scar on the growth ring and determining the seasonality of the fire activity. And the information they came up with was that 56% of the natural fires occurred during the spring months, 38% during the summer, then only 6% during the fall. And prior to that time, the primary prescribed fires were being conducted here during the fall months. But with this information, plus we had some data from fire effects monitoring plots, why by no means comprehensive, it at least suggested that there may be some issues with non-native and exotic species associated with the fall burn. Because of those two things, we began shifting our prescribed fire program to try to take advantage of spring burn windows whenever possible. Upper Friholies Canyon was a keystone to our fire management program. That's the canyon that during the 1977 the Mesa fire, the fire across that canyon and spreading through the park and onto the lab lands. And then in the 1996 dome fire, in 1997, Loomis Wildland fire used, a great deal of time and effort and concern was keeping these fires out of Upper Friholies. That served as a major pathway. Once it got fire, it got in there, it posed a serious threat to the town site and to the laboratory. And in fact, you have a chance to see it when you go from here to stand two.  Hasn't seen any fire since the late 1890s. Around 1995, a prescribed burn plan was prepared for that unit, Unit 9. And in my arrival, the more I looked at that plan and the more I looked at that canyon and walked around, the less comfortable I was, is my ability to be a burn boss to be able to pull that thing off. But we were very fortunate to have someone at the caliber of Paul Gleason in our Intermountain Regional Office. So in the fall of 97, I talked to Paul, said in the burn plan, he and I talked about it for a while, and he agreed to be the burn boss for Unit 9. And that was the only reason that he was actually here in the spring of 2000 for Serro Grande. He wanted to come down, do an on-site review of Unit 9 before he revised the burn plan for that. And he hoped to be down here when there was actually fire on the ground from a prescribed fire or suppression activity so he could see burning conditions firsthand. There were two other burn units that were located upslope and downwind of Unit 9. That's Unit 1 and 5 that also became the Serro Grande fire. And it was apparent that you could not put any fire into Unit 9 until you treated those lands that were upslope and downwind. This talked just a little bit about the weather and what was going on there. During the fall and winter of 99, 2000, it was much drier than normal in here below normal precip. But as we started getting into mid-March into mid-April, we got increased precipitation. And during that one month period, an on-site weather station located on the burn unit measured almost an inch and a half of precipitation during that month. That included a 16-inch snowfall on Serro Grande. But because of that snow in the precip, our plans to do the burn in April had to be put on hold as the unit was simply too wet to get anything accomplished. But by mid-May, excuse me, mid-April, there were prescribed burns being conducted at the lower to mid-elevations. On April 24, Santa Fe National Forest conducted a burn south of White Rock, the community you passed on the way in. And then on April 25, Bandelier ignited Unit 40, which is 350 acres, around the headquarters campground residence area. And both of those burns were successful. No extreme fire behavior was observed. No significant holding problems were encountered, either on the Park Service burn or the Forest Service burn. On the afternoon and evening of April 28, a little system came through. And it was a little dry lightning bust that resulted in a half a dozen or so new starts right into Serro Grande vicinity, kind of that higher elevation, 8,500 to 9,500 feet. Some of the initial attack actions were delayed, because it occurred late on the 28th, didn't get resources out to the 29th. But in spite of that delayed initial attack, all the IA actions were successful. All of those fires were suppressed at less than an acre, except one that went to four acres before being contained. And again, no extreme fire behavior or anything was observed. So based on what we saw in the previous burns this week earlier, and what we saw at the higher elevations during the initial attack activities, it seemed to indicate that there was a low probability of having extreme fire behavior on the Serro Grande unit if we were gonna ignite that in the next few days. On May 3rd, touch bases with Mike Powell, Mike, everything sounded good for Serro Grande as a go. One issue that he did have was Forest Service employee had lined up to be the holding boss. Wasn't available to another assignment. He asked if I'd be able to assist in that capacity. And I said yes. On the morning of the 4th, we went into the office, checked the situation report. There was one type one incident in Arizona and the Southwest. There was some scattered initial activity, initial attack activity, but nothing other really substantial going on. The preparedness level for the Southwest was in preparedness level three at that time. And that meant there were no restrictions on prescribed fire activity. So later on in the day, Paul Gleason was here, met with Paul. We went out and did a recon on the ground of burn unit nine.  And so with that, that's the end of the introductory chapter. Again, you'll learn more about the prescribed burn plan and other things in the next stations. So hopefully, I've adequately set the scene for ya. And at this point, that's open it up for questions.  In other words, that many phases, that many units, that many acres over that many years, was that, was this the big one, so to speak? No. Or the ones prior had equal in landscape, equal in complexity, equal in duration, et cetera? Yeah, prior to 1976, or 1996, that wouldn't have been true. But around 96, there was an effort to try to, instead of doing 200 acres or 400, of trying to get larger units, and there were several thousand acre, I mean, two or three thousand acre burns that were done 1996 through 99. So there were others of similar size, duration, that type of thing. And they were fall? No, they were spring burns. Spring burns also. Yeah. Yeah, once we started getting that new information and started shifting to the spring burn window, I think we only did one fall burn, maybe from 97 to 2000. The rest were all spring. What I'm here to talk to you guys about is the development of the burn plan, fuels, weather, and prescription. At the time of project initiation, as I said, I was scheduled to be the ignition specialist. I was fully qualified in that capacity and had run about somewhere between 25 and 35 operational periods as a type two ignition specialist at that point, mostly in the Southwest, but some in the Northwest. The prescribed fire project area represents about a thousand acres. Couple lines on this map are a little misdrawn. This Eastern flank actually drops through this meadow and then parallels the existing North Eastern boundary that you see on the map. And if you turn around, you look at this fall summit right behind you is this knob and the montane grasslands. The actual summit of Cerro Grande is the far peak that you can see the tree wall standing just on the skyline with the grasslands underneath it. A unit was gonna be treated in three phases. Phase one was burning in these montane grasslands. This was gonna be, and as you look at this, phase one and two essentially represent a blacklining operation. Phase one to treat the montane grasslands in the top. What we were gonna do up there, burn that at night, put the back edge of it out to establish a black line along the top of the unit. Phase two would have brought fire down the flanks of the unit. There was a saw cut coming off of this meadow, tied into some old roads that are very grown over now. We opened some of those roads back up only for holding lines. This is wilderness, we did not wanna use vehicles off the roads anywhere in the park. That's consistent with the resource management plan in the park. So saw cut established down through here. Phase two would have blacklined both sides of the unit. Phase three would have been a final after a black line's established, burning out the interior in these Aspen communities and some of the heavier fuel model eight. This could have taken place, the way we'd written the plan could have taken place over a period of weeks, perhaps as much as a month, month and a half, depending on seasonal conditions. We'd written the plan to allow us to go up into those montane grasslands as soon as snow came off them, even if we had snow in the spruce forest underneath, if we still had drift snow in there, we were gonna get up there and do some burning and felt like we could hold on to it real well.  And we had the best luck with spruce bows when we did it. Michael talked more about that during operations. We had taken two of the module members from the Bandelier fire use module, put them up on the hill until about 2,200 hours on the night of the third to collect data for requesting a spot weather forecast the next day. Within that, Mike Powell called Chuck Maxwell, who was the forecaster that we worked with a lot at the National Weather Service Office, asked him if the models he was looking at were showing him that the next night would be well represented by weather that we were pulling that night. Spot weather forecast was requested at 11.35 on the day of the fourth, and we got it back. Everything looked go. Morning of the burn, we made our phone contacts. I made about 26 phone calls that day. Called everybody from Cochatea Pueblo to the Santa Fe Forest, to our local cooperators, the Baca, State ADQ. We checked on the availability contingency resources. Knew there was a tanker sitting on the runway in Alacurkey. We knew that Sandia Hell Attack was sitting on the pad at Tejeras. I actually checked specifically on the Santa Fe shots. They were in station and not committed. And there was another Type 2 crew available from the BIA within the area. We were told that all contingency resources could be delivered within our time frames. Can you just show me where in the face, to where the hand line went down? There was, as I said, there was a saw cut established from the edge of this meadow that bounded the burn unit. Again, this is incorrectly drawn. It actually came off like this. Saw cut tied these roads in. And the plan was just to keep, as we, after we got that saw cut in, we were gonna keep up with building hand line as needed, check line as needed, as we burnt down through this fuel model eight. There was no scrape put in, but there was a sizable cut. There was a risk analysis done. There was a complexity rating sheet done. At the time, as you'll recall, we didn't have a standard. There were about three complexity analysis out there. The one that Mike elected to use was the one that Rocky Mountain National Park had been having pretty good luck with. It's here and available, if any of you want to look at it. And looking back on them now, they're all pretty awkward documents. And I really feel like one of the good things that came out of all of this was we have a much better system to plan within now. It's across the board, standardized. I think it's a pretty good system and it's a lot easier to use than it used to be. I mean, some of the stuff, frankly, that we had to work with at the time was kind of voodoo. Quick introduction, I'm Mike Powell.  My position at Bannel Air at the time was as temporarily promoted into the assistant fire management officer. My normal job was a fire use module leader at the park here. A few kind of quick orientation things. You can actually now see the top of Sarah Grande up there. And then pretty much the burn, pretty much follows that ridge line down, goes up to the top of this hill and then kind of heads down, eventually ties into the road that direction. On this side, if you're in the right place, you can see the saddle over there. I don't know how much Matt talked about that, but you can see the saddle over there. It goes up to another ridge and then drops back down pretty close to where Matt was down there. We conducted that briefing about seven o'clock that evening after the briefing. Al King called the national weather service on his cell phone and just confirmed that their spot forecast was still looking good and pretty much the weather service confirmed that it was still looking good. At that point in time, we did start a test burn. It was about 20 after seven when we actually started the test burn. The fields at the very top of this hill were pretty light. And to me, it wasn't real representative of what we're gonna be burning in. So we actually continued the test burn for quite a ways and it took a fair amount of time. We actually stopped the test burn about eight o'clock at night, but we stopped it once we got to see fire behavior and fields that we felt were representative of the entire area. As we worked down, it took a while. Like I say, this is not a short distance clear across that thing. Eventually they got up there. They swatted out the little piece that needed to be swatted out and they started ignition down into the saddle. As they're bringing it down to the saddle, there's still, I think there's just four people left on this far side. Their continuing ignition, you know, at a quite a bit slower rate, pretty much taken really small chunks, but there's still continued ignition at that point in time. I pretty much stayed with the ignition down into the saddle, like say down into there for a ways. And at one point in time, the people on the east side, they called up and said, hey, we're gonna stop ignition. Pretty much what ended up happening, the winds are generally out of the Northwest up here. And as actually you could start, if you look at how things work, as you start turning around this corner, the winds will actually start pushing actually towards the line out there. So they pretty much stopped ignition at that point in time. And I decided to go back and see what was actually happening over there. I remember Ed Hyatt, he asked one of the Black Mesa crew members, probably three different times to do something for him. And that guy was sitting on the ground and he was just very slow to respond. And it was at that point in time, I said, hey, I'm gonna send these guys off the hill and we're gonna keep the Park Service people out here for the night. They were still igniting down into the saddle at that point in time. That was about midnight when I made that decision. As pretty much the people on this East side were still, they were sent down the hill pretty much at that point in time. A few Park Service people were sent down with them so that we'd have some people up there, at least some Park Service people rested for the following day. And you had the opportunity to work with that crew and with prescribed fire operations prior? Not that crew. We actually used some Black Mesa crews on the previous burn we did a couple weeks earlier and they were actually really outstanding crews, but they had sent crews someplace north and pretty much we were down to the last 10 people they had from the way I understood it. The people down on this side, they're still doing ignition down into that saddle. About two o'clock that night, they had completed their ignition and released a Black Mesa people down to the road. It was at that point in time that I actually left the unit and I went down to go order resources. Went down to my office, I called up dispatch and said, hey, I need a crew for our burn. Their initial response was, you need to type one or type two crew. And I said, yeah, type two crew would do us. And they said, well, I'm gonna have to talk with my supervisory dispatcher about that. And I said, well, can we talk with him? He goes, well, he doesn't come on until eight in the morning. At that point in time, I was pretty much boiling. I did get hold of the engine crew here at Bandelier and had those guys, they were supposed to be reporting out here at six o'clock in the morning the next morning. At that point in time, I called up the people back here on the unit, pretty much let them know what was happening and told them that I was gonna get some sleep so it could be available in the morning. I went down to went to sleep and six o'clock in the morning, Paul Gleason comes in, starts waking me up. And I'm pretty dang drowsy at this point in time too. He goes, hey, and he says, hey, it's backing down the unit, backing down into the unit, you know, pretty much quite a ways we need to do something. He's like, oh, okay. And he's like, well, what have you done? And it's like, and I start telling him what's happening and he's like, okay, well, we need to do something. And he says, okay, so I get up, I call dispatch again. Phone rang 10 times and I actually didn't get a single, didn't get an answer out of it. At that point in time, Paul suggested, okay, we need to start calling people, call the superintendent, call some of the regional fire staff, you know, just start letting people know what's happening out here. So he started making those phone calls. About seven o'clock I decided to call dispatch again and did get the supervisory dispatcher that time, let him know what was happening. At that point in time, Paul said, hey, we need to type one crew in a helicopter. And personally it sounded like gravy to me. It's like, yeah, if we could get that, I had some doubts whether we could get it after the first dispatch experience, but called dispatch again, talked with the supervisory dispatcher, said we need to type one crew in a helicopter. He said, well, are you declaring this wildland fire? And I said, no, we're not. Then he asked why and explained, hey, it's still within prescription, still within the unit, we're not having problems. We just need the resources to make sure that we can deal with what we got out there. So your initial thought to at 3.30 in the morning to start ordering some resources, was that because you had to send down the Black Mesa crew and so your kind of your nighttime plan was not going quite the way you wanted it to? Yes. Okay. I'd talk with dispatch, they were questioning whether I was questioning my resource orders. They called up Al King on the burn unit and pretty much asked him. And the way I understand it is that Al pretty much gave him the same information I did. If we wanted those resources, wanted those resources, we were not declaring it a wildland fire and but we did want those resources. Dispatch called me, it seemed to me it didn't take very long from my conversation to when they called me back probably 15, 20 minutes. They called me back and said the resources were coming and they should be there by nine o'clock. And then of course they Santa Fe hot shots and helicopter three zero something. I can't tell you exactly what they were anymore. But those resources were en route at that point in time is what they're pretty much saying. That point in time we went up to TA 49 and started talking with the fire, finding out what's happening. I believe it's around 10 o'clock. Ed called and said he was having problems or had an escape on this side. About that same time, the helicopter did start arriving. And they landed on the ground and we're doing their helitex stuff. And we're talking with them about what's happening about the recent escape and everything and kind of got them lined out to some extent. And Paul came up to me and said, hey, Mike, why don't you go get some sleep and let me take this over? And I said, okay, it sounds okay with me. So at the point where Paul took it, were you guys, were you getting uncomfortable with things or were you considering conversion? The escape had happened at that point. Okay, and was that significant enough that you were considering conversion? I don't think I was in reality. Part of the information from Ed that was coming down is like, yeah, I think we got it. No, then the next thing would be, no, we don't got it. And then another one, oh, I think we got it again. So it was kind of hit or miss. So things were fairly uncertain at that point. Yeah. Mike, did you guys work with dispatch to ordering resources for support to prescribe fire before or only in support to suppression? So spread? It's very interesting. Yes, we had worked with them with prescribed fire. There were problems. And I don't believe it's just within this zone. I think within this region, I believe there's problems with ordering resources for prescribed fires. And when I was with the fire use module, as all prescribed fires, and it's all this constant hassle. It's like, yeah, where's this resource or blah, blah, and of course we know three days before it's coming. And it's like, hey, tell people, hey, we're expecting things. And then the other side of saying, yeah, we sent it. And then people are trying to track things down, but there was always problems. Mike, could you describe the fire behavior again? I mean, just what it was like? It's generally low. Like I say, average flame lengths are probably about a foot and a half. The, you know, you'd see three-foot flame lengths occasionally, occasionally we were getting trees torching. Spot fires? No, no control problems. Like I say, is the swatting and spraying with the backpack pumps worked really well. Yeah.  Occasionally they'd have to do something, but they weren't running back 100 yards of chased spot fire or things that kicked up again. So the next day, if I understood, you got a helicopter coming in and another crew, right? So how many total people are on the hill holding them? At this point in time, there's one, two on this side, and I think there's four on this side. So there's six people up on the hill. The two people from the engine crew arrive, so there are eight, and there's gonna be an additional 20. You know, working around in your wildest imaginings, could you've ever seen this thing blowing up and making its way to Los Alamos? Did that even cross your mind, do you remember? You know, it did not. Yeah, a lot of it, too. You know, we were collecting fuel samples here. To me, it's like, you can look at the weather stations, and they kind of give you an idea, but we're collecting on-site samples and collecting a decent number of them.  The other side's northeast-facing. You know, it's like, it really was not in my wildest imagination. So at about 0700, we're up moving around, we're watching fire, and we knew that the Engine 9-1 crew was gonna be coming up to help us that day. What I was starting to see up there was that this fire was backing down as it should have, just backing down pretty slow, but my worry up in here was that I was gonna start to get hooked on my holding assignment up here, and I made a call on the radio to the folks on the other side, and Al was over there, and my suggestion was, let's just take fire a few feet at a time, is what it amounted to, and just keep it even as it backed down the hill. At around 100 or so, you know, give or take, right down in the middle of this, there's a little bit of a saddle in this that you can't tell, but there's kind of a depression that sometimes has water in it, and we were just taking a break there.  And a couple chains up in here, I could see flames that were maybe an inch or two high. I mean, barely enough that was visible, but it was right in that area where we had black line, and it was starting to creep out into this grass out here.  By the time I did get up there, it was, you know, a few feet across, spraying at it, and it's flaring up and starting to move a little bit, and it's in that little bit higher grass, and that just created a little bit of a control problem for us. So we continued working on that for a while, and it's gradually, it's getting bigger and bigger, and it's probably up to a half acre or so. And I called Al and said, hey, we've got a slop that we just cannot hang on to. I need some help. I need, you know, and it was something like, well, what kind of help? And I'm like, I need a helicopter in a bucket would be best, you know, and we need them now. So that's the kind of stuff that was going on. We were, we started using regular hand tools and they weren't really effective in the grass. We found a great big fir tree up there and just cut vows off it, and we would beat those things until there was nothing left on them until it was just a stick, you know, and that's what we did for quite a while. And then the helicopter arrived up to Bandelier. And what I wanted was a helicopter in a bucket. That's what we needed was we needed some water up there. But what ended up happening with that is the helicopter came up with two crew members and a manager on board. And they dropped the two crew members off right here in this meadow. And it was like, hey, I need water. I don't need the crew members. I need the water, but I'll take them. I mean, they're here. I'm not gonna get rid of them at that point. So I put them to work on this east side. They're putting in some line and trying to, you know, they anchored in and we're moving along. Helicopter lifted off with the manager. They went, it took them a while, but they found a water source out in the Baca, just a mile or so away. So that's, you know, there's another one of those little small pieces in the puzzle that was being delayed as we needed the water and they needed all these other things. So they got the water, they got the manager out. They got a bucket on board and they started making drops. And the drops were doing pretty good. But, you know, imagine a Type 3 helicopter with a small bucket that's already been cinched down for flying at 10,000 feet. The, where the drops were hitting was effective, but by the time we get back with the next bucket, things were heated up again. So we were making a little bit of progress, but at the same time, we were getting beat. I mean, I had spent a lot of hours up and had already been working on these spot, this spot or slop over for quite a while. So that takes us up to about 11 o'clock, you know, with our burning, having the slop, the helicopter coming in, the two crew members getting the bucket drops. And about 11 o'clock, the shot crew, I believe, was getting parked and getting ready to hike up here. So we're, you know, we're feeling pretty good. We got, you know, guys, we all know the crew just down the road, they're gonna come up and help us out and things are looking all right. So we, you know, in between 11 and about 12, quarter to 12, something like that, between the crew got up there, we just continued on trying to catch this little slop over and some places we were doing pretty good and some places we were just leaving it alone because we weren't effective at it. Could you refresh me what the contingency resources were identified as and then I've got a follow-up to that? A helicopter, an air tanker, and I think T-Cruise was the daytime contingency. And that was for phase one or the entire unit, the entire burn, that was a contingency for the entire plan. And the trigger for that, for the contingency resources, was basically the release of the Black Mesa crew. And at that point, Mike's whole rotation, everything that he had worked out as far as cruised the holes were denied, people to come back during the next day operational period. That's where that kind of needed some readjustment. And so that's what we needed, the contingency resources to bump in for the next day's peak burning period. The fire behavior and, I mean, it was kind of tracking within that, you had a pretty wide prescription, right? I mean, it looked like there was pheromona leeway and it was all within that. No bells were going off in your head other than maybe the lack of resources to hold. Yeah, it wasn't so much an alarm bell, but certainly it was very paramount in my mind whenever we released Black Mesa and knew that Mike's crew rotation had gotten kind of followed up because that that we were gonna have to have additional resources to hold during the burn period. But it seemed like with him going down, we had a contingency resources in place, et cetera. We thought that that was all gonna go pretty smoothly. Get those guys out here and up on the hill by 10 o'clock, 11 o'clock when things started heating up. Again, at 10 o'clock had the call from Ed that they had to slop over out there, needed the resources. We knew that the San Diego ship was inbound. Check back with dispatch again. They said their ETA should be eminent.  There was some discussion of, well, we need a helicopter with bucket in four years and thinking back to it all. I don't know if someone specifically, what their specific, what they heard on their side as far as, okay, do we need a helicopter with bucket or do we need to come up there with the bucket ready to go? Not sure, but anyways, helicopter arrived. There were some issues initially with dip sites. Had to work through that with said, if a dispatch and the Lano EOC to make sure we could get the dip site squared away, not that squared away, they started dropping water. The reports of us hearing from Ed on the radio was, it was kind of intermittent up. It doesn't sound very good. Next time, well, it looks like we're making some good progress. Things are looking pretty good. And then the shots arrived at about 1110 is what I had logged in. They arrived down here on the road. And we had also the Park Service Resources that Mike had released the evening before to go down the hill and get some rest. We also had those folks come back up with the shock crew to supplement those people and to make sure they could get into where they needed to get to. We didn't wanna have further delays of them not knowing which trail to take up or whatever. So had the Park Service folks come back up, majority of folks went over to the east side, had one squad come over to the west side, that we would get pretty late and our tour duty needed to get swapped out. And then also the rest of the unit where we had checked on that once earlier in the morning, we needed to have somebody over on this side just to keep an eye on the rest of that unit so there wouldn't be any other sloppovers or concerns. And then around 1,300 hours, got a radio call from the shot superintendent saying, well, guess it was, why don't you point about where it was? Your unit would have exactly where? About 1,300 where they started running their problems in order to. At the time when the shots showed up and things, the resource, who was the incident commander? At that point it wasn't, it was not a declared and escaped prescribed fire. It was still being managed as a prescribed fire. We thought we could catch this sloppover within the Bergen unit perimeters, catch it, contain it and continue on with business. So Paul Gleason was the burn boss. And I was serving it. I'm a burn boss, I'm sorry, I used the wrong term. So again, I'll go ahead. I actually met and briefed the shot crew right about in here. This meadow actually kind of continued down in along this line and you can see this line in here. So that's where I briefed them and that's where they anchored in. So anyway, it's 1,300 hours while the shots were trying to get hooked around that. I got a call from them advising that the fire had gotten into the trees, it's torching out, starting to move through the crowns and they're requesting an air tanker. About the same time, there was also an aerial recon that was up to the Forest Services launch for detection and to just, you know, see what's going on up here and talk with the aerial observer and they confirmed, yeah, looks like you guys are gonna need to have some mud on this thing. So called down the Gleason and Paul was right there with the agency administrator rep and the three of us jointly decided that this was our trigger point that this thing's no longer in prescription. We're gonna have to call an escape and let's get the air tankers ordered. So that's what we did. And then I guess the story after that was with the air tanker drops and the shock crew they did contain that slop over at about 30 acres by the evening, that would be Friday evening, at 30 acres and there was a one acre spot on the forest, the rest was all on the park. And but again, you know, for the staff ride, that's basically the end of the story because we had declared it at that point. Two or three quick items. Number one, that whole thing was a very professional effort and it was based on logic and professional rationale. And I think in terms of what happened, it was easy to see myself having been a part of that. Either had I been there to be a part of it or looking back over my own personal history to say I was a part of something similar. Also just a couple of things to repeat. I also could see myself in that same position and appreciate the folks coming out and talking with us about it. I also was struck by the fact that it is hard sometimes to look back because some of the changes or some of the issues that we deal with today are a result of Sarah Grande and we may not, you know, in some of those cases, we may not have the same issue today because we have made some changes institutionally. I'll tell you, I just, a lot of respect for what you all do. And again, coming from the wonderland of local government and I mean, I work for LA County. You know, you were saying, I think at one point there was like 130 some people on the fire. We call for a first alarm brush, we got 141. You know, so it kind of boggles the mind, the kind of work that you try to accomplish or that you do accomplish.  I think the most pivotal thing for me at the beginning of the staff rise when Al King just said really with all his heart how tough it was for he and Matt and the others to come back and for the fact that they were doing it just so they would hope to help any of us in this room for preventing to go through what they went through and that kind of took me through the rest of the stations. I was burning in a park, in a park in the Southwest same time periods as Bandler was doing their thing and I, through all those stations, I could definitely see myself in the same shoes as all those folks had been in. So I really appreciate that personally. I'm looking at this crew that had the willingness to come back here and talk to us yesterday and you know, when Al King kicked it off, you know, there was partly being responsible for organizing this thing, there's always the nervousness, is it gonna go right? And two sentences out of Al's mouth and then through the rest of the day, it was obvious it was working. But what the feeling I had was the incredible feeling of pride to be even shoulder to shoulder with a group of people that were willing to come back, having the courage to come back and talk to this. And just knowing what you guys must have went through without asking you to know that, you know, in a way you were responsible for lighting a burn that was ripping into one of the largest nuclear facilities in the United States, you know, had burned homes. I can't imagine that feeling. So, you know, just doubly emphasized for me that your courage in coming back was just outstanding. It sends shivers up my spine to know that I work with people that are this professional. I knew a little bit more about Sierra Grande than I guess the average Joe, because I was on one of the Type 1 teams that helped put it out. I learned yesterday a little bit more and I think maybe we need to find a way to set the record straight, because what I know and what the report says are two different things. And I think maybe lessons learned might have a role in that. It's been my experience with other staff rides where we still have folks that have been involved that come to the site and present their perspective. Two things, we have to be very careful how we formulate our opinions and perceptions based on reports. Those reports are instigated under a different concept than how we look at them as professionals. And so it would affect, it has affected my perceptions and then how I carry that perception into doing my own job. I think the whole investigation process needs to be revisited because I think we all know escapes are gonna continue to happen and hopefully not on this scale, but I'd like to think that some higher ups are maybe planning ahead and thinking how are we gonna do this and how are we gonna protect our employees and not abandon them? There are a couple of folks who had the courage to stand up and back and support folks taking care of their people, making sure that political processes didn't run roughshod over people that were trying to do the right thing. People like Tim Saxton stood up and put their careers on the line. And so there are leaders among us that have courage and have the right stuff and they're present with us. Some of the leadership that we wish would be more involved, more visible, providing psychological safety to folks is waiting, I think, for something from the field to tell them that this is important. This workshop has the opportunity to provide a lot of that impetus to them and make it clearly a message that they would be then willing to listen to. Based upon what we heard yesterday in the reading before the class, I picked up on something that I think is a significant systemic failure on our parts and that's the dispatch organization and their response to the burn boss. I've dealt with this myself several times where I work and it is not the responsibility of the dispatch organization to determine whether or not resources are needed or how they will be paid. That's a question that's up to the agency administrators and budget and fiscal folks that burn boss should have been responded to immediately and should have had the resources that they need. Whether or not it's a prescribed burn is irrelevant. What was relevant was that there was fire over a ridge from the Los Alamos National Laboratory and having to check with one supervisor in that situation is a time lag that isn't necessary and I think that's the main thing I'll take back with me but I do think the folks conducting the prescribed burn did everything that they could and I probably would have made the same decision. I'm a local government fire chief and we do micro burning, meaning that we do it on a small, small scale. We burn in small increments next to homes, of course but we staff it with three to four times the staff and what we're seeing with you guys. I think you need to take a look at it from a risk management point of view and take a look at how you're staffing, what your contingencies are and are they in place to do the job. I don't know how you guys do this. I mean, I wouldn't have, you know, we wouldn't, Norm and I were looking at that, we wouldn't start this thing, we were, you know, we would need 10 to 15 the amount of people. Now that's standard local government attitude, I know. Understand my bias but at the same token I think there's some merit to that and there's something you should take a look at is how you're staffing, what your contingencies are and are they truly in place and is there truly enough folks on the ground who do the right job. Some that struck me really hard yesterday and I think it's still a huge problem for us is the concept of contingency. We had a big rug yanked out from under us with the air tankers and how many of us have written burn plans where that's the contingency to load and run retardant of some sort, whether that be a helicopter or an air tanker and I go, where are we gonna go? What is our contingency? And it keeps coming back to that very same discussion as L.A. County can call and get a first alarm and get 144 people. We were asking for one hand crew. Where are our contingencies and what are they gonna be here in the future and how are we gonna play this game out with a dispatch is I'm really concerned about that. I'm reminded, it was reminded again yesterday of the inadequacy of the national prescribed fire curriculum. It needs to be adjusted, needs to be overhauled. I don't think that it addresses landscape scale burning at all and I think there's some major things in there that we need to deal with. Again, the policy, we need to develop a policy to protect our employees during periods of time when we have an incident like this, we need to protect them from the time the problem occurs through the end of an investigation to attempt to minimize the amount of influence politics may have and ensure a just decision is made on employee welfare. What I came away with was, I would have implemented that burn also if I was a burn boss. Operationally, yes, I would have done things different and what I saw was it difficulty to analyze risk and everything we do is how we look at risk, how much risk we're willing to take, why we'll take that risk and it's very difficult for us to get a true handle on what the risks that we're taking are and then why are we out there taking that risk? What reward do we get? What benefit besides that it's just our job to do this? So I would have taken that risk, yes, because I'm a risk taker as most people probably in this room are and yet our agency now, we don't reward people for taking the risk, we always come back and look at when there was a problem and we don't come out and look at the good successes. How many workshops do we have to see, geez, they accomplished 200,000 acres, they did good. Now we'll come out and we'll look at the problems. So I think we need to change a little bit and start rewarding people for taking the risk and even when the circumstances go bad. I think sometimes with the situations that we are dealt with, I'm talking here about the shape of the ecosystem and the landscape, how we have a lot of conditioned class three that we're trying to do something with. A tendency for a lot of agencies, mine included is to go out there and fix everything right away. And I think there's a political emphasis there also. I don't think that that's quite the thing to do if you have us, an area that is supposed to burn, for instance, once every five, 10 years, hasn't had any fire in it for a hundred years.  I don't know if we're doing the ecosystem right. I don't know if we're doing our personnel right, asking them to do that. I think trying to meet all your objectives all at once might be something you need to reconsider. From a lessons learned perspective, it was very interesting because I had folks come up to me that were in our group that said, of all the different lessons learned that this type of thing, a staff ride like this was the best way for them to learn. And thinking about this last night and today, like to pass on a couple other impressions that I had. And one of the things is that I really felt yesterday went well. It went better than, as you prepare for something like this, you kind of go through various scenarios in your mind. And it exceeded my best case scenario of how it yesterday would have gone. And I'm very pleased with that. And I think some of the reason for that success are the participants, the rest of the folks that are in this room. You guys were really engaged. There was no doubt about that. You asked good questions. The focus was on learning lessons. And there was good dialogue. And I really appreciate that because I know for myself, I felt very comfortable with you. So thanks for that. I really appreciate that. It was mentioned yesterday by one of the presenters. They were thankful. They had an opportunity to tell their side of it. And certainly considering all the liability that is surrounding these folks and their agencies, it's understandable not to want to say a lot, but it's important to them and it's important to us as a profession to hear their side of it and to present it in a form where they can feel safe to be able to do that.


Welcome to the 29th lecture in the course engineering electromagnetics. In this lecture we continue our discussion on rectangular wave guides which was initiated yesterday and we talk about the TM MN modes and then go on to discuss the TE MN modes. First we have a quick recapitulation of what we did in the last lecture. We are considering the rectangular wave guide shown here consisting of perfectly conducting walls located at x equal to 0, x equal to a and y equal to 0 and y equal to b. To find out the properties of the wave types supported by such a structure we first wrote for the interior of this wave guide the Maxwell's equations expanded these Maxwell's equations in the Cartesian coordinate system and then assuming that the wave propagates along the z direction we simplified these by substituting for del by del z the factor minus gamma bar. Then these equations were further ordered by expressing the transverse field components in terms of the longitudinal field components that is x y components were expressed in terms of the z components and then we were able to make out that we may either have TE type of solution or TM type of solution. We considered first the transverse magnetic type of solution where hz is 0 and ez is non-zero and we obtained the following solution for the z component of the magnetic z component of the electric field that is C sin of m pi by a times x sin of n pi by b y e to the power minus gamma bar z. The indices m and n decide the order of the particular mode and therefore this becomes one of the field components for the transverse magnetic modes and we call this TM, Mn modes. The first subscript m indicates the order of variation along the x direction and the second subscript n indicates the order of variation along the y direction. We can now complete the field expressions for the TM, Mn modes and for the sake of brevity we rewrite ez in terms of the constants a and b so that it becomes C times sin of Ax sin of Bx sorry times sin of Ay e to the power minus gamma bar z. Then using the expressions for the transverse field components which are available in terms of the z components here hz is 0 and we have expression for ez available and therefore we can find out the expressions for all the remaining four field components. The steps are fairly straight forward and therefore we can write down the field expressions straight away. We get Ex equal to minus gamma bar C by H squared then B cos Bx and sin Ay e to the power minus gamma bar z. Then Ey comes out to be minus gamma bar C by H squared A times sin of Bx and cos of Ay e to the power minus gamma bar z. Hx comes out to be j omega epsilon by H squared times C and then A sin Bx cosine Ay e to the power minus gamma bar z and finally Hy comes out to be minus j omega epsilon by H squared times C and then B times cosine of Bx sin of Ay e to the power minus gamma bar z. This is the complete set of fields for the transverse magnetic modes with order m and n. One can make out from these expressions and recalling that B is equal to m pi by A and A is equal to n pi by B that the lowest value of m or n which is required so that these field components do not all become 0 is n equal to 1 and n equal to 1. If either of these becomes 0 the way A and B appear in these expressions the entire set of fields becomes 0 it vanishes. So from this point of view we make this observation and it will play an important role later on that the lowest order Tm mode is Tm 11 where m is equal to 1 and n is also equal to 1. Neither of these can become 0 if that happens then the entire set of fields vanishes that becomes a trivial situation and therefore for a non-trivial situation we must have both m and n non-zero and then the lowest values possible are 1 1 each. So Tm 11 is the lowest order Tm transverse magnetic mode. Before we discuss the properties of the transverse magnetic waves let us also complete the similar exercise for the transverse electric modes. And we proceed in a manner similar to what we did for the transverse magnetic modes for the transverse electric modes the electric field is completely transverse to the direction of propagation and therefore we have E z equal to 0 and of course H z not equal to 0. Once again if both become 0 then the entire set of fields vanishes which is not a situation of interest. So we will consider the component of the wave equation for the magnetic field which involves the z component the H z component and then using the method of variable separation we will obtain a solution for H z alright. I think we can write down the solution straight away since the steps are completely in parallel and therefore H z not the part that varies with respect to x and y turns out to be c 1 cosine of b x plus c 2 sin of b x into the second part is c 3 cosine of ay plus c 4 sin of ay by using the method of variable separation we can reach this stage by following the steps previously described for the Tm modes. Now the question comes how do we apply the boundary conditions because H z is not a field component is not a tangential field component to the perfectly conducting volts and therefore we calculate the field components the electric field components in terms of H z which are tangential to the perfectly conducting volts. For example we can calculate using the expressions for the transverse fields in terms of the longitudinal fields E x and E y E z is 0 and in terms of H z we can write their expressions and E x and E y are going to be tangential to the corresponding perfectly conducting volts. So on E x and E y we can apply the boundary conditions that the tangential electric field component on a perfect conductor must become 0. So in this manner we apply the boundary conditions and we write for E x or to be more precise for E x not we write minus j omega mu by H squared times del H z not by del y and as you can make out the superscript not stands for the fact that we have removed the factor into the power minus gamma bar z because that is common on both sides all right. And similarly we have E y not equal to j omega mu by H squared and del H z not by del x all right del H z not we have just written and therefore these expressions for E y not and E x not can be obtained carrying out this procedure E y not will come out to be j omega mu by H squared and then B times the derivative of this first part and the second part is not going to be affected because it is the x derivative which is involved and therefore we write here minus C 1 sin of B x plus C 2 cosine of B x and this part we write as capital y because before reaching this step one would have written H z not equal to x times y and as a solution of the wave equation x comes out this and y comes out this and y is not getting affected in this operation therefore we retain it as it is which should be 0 wherever it is tangential to the perfectly conducting boundary walls of the waveguide that is at x equal to 0 which implies that C 2 should be 0 similarly it should be 0 at x equal to A and as before that implies a particular value of B that is B equal to M pi by A in this manner we have evaluated C 2 and we have got definite value for the constant capital B similarly taking care of the other part that is ex0 we get ex0 equal to minus j omega mu H squared and here the first part that is capital X is not getting affected and therefore we retain that as such and the second part gives us A times minus C 3 sin of A y plus C 4 cosine of A y which is tangential to the other two walls of the four walls of the rectangular waveguide and therefore we can get some more information about the remaining parameters it should be 0 at y equal to 0 implying that C 4 should be 0 and similarly it should be 0 at y equal to B giving us a certain value of capital A which is N pi by B where M and N are integers taking on values 1, 2, 3 of course whether they can take on the value 0 or not we shall discuss in a moment alright so based on this we now have an expression for H z0 which can be substituted in the expression in the expressions for the transverse field components and then one will get the complete set of fields for the TM modes so carrying out this procedure we get H z the complete expression for H z as equal to a constant C where we have clubbed C 1 and C 3 together C times cosine of B x and cosine of A y and of course e to the power minus gamma bar z which becomes the starting point for the field expressions for the TE modes and depending on the values M and N it becomes the TEMN so for a TEMN mode the z component of the magnetic field comes out like this and then using the expressions for the transverse field components in terms of the longitudinal field components E z is 0 and H z is now available so we can get the remaining four transverse field components and we write down these field expressions as follows we have E x equal to j omega mu C by H squared A times cosine B x sin of A y e to the power minus gamma bar z E y comes out to be minus j omega mu C by H squared B times sin B x and cosine A y e to the power minus gamma bar z H x comes out to be gamma bar C by H squared B sin B x cosine A y e to the power minus gamma bar z and finally H y comes out to be gamma bar C by H squared A times cosine B x sin A y e to the power minus gamma bar z a very high degree of symmetry is obvious in these field expressions and H x and E y behave in a similar manner as far as the x and y variations are concerned and E x and H y behave in a similar manner which will have a bearing on the wave impedance which we shall calculate later on and of course all field components vary along the z direction as e to the power minus gamma bar z corresponding to our assumption that the wave is propagating with the propagation constant gamma bar in this z direction one can look at these field expressions more closely and make sure that each field components satisfies any boundary conditions that are applicable on that particular field. So it becomes a consistent set of field equations which satisfy of course Maxwell's equations and also the boundary conditions which are applicable in this case and since E z is 0 it is a TEMN mode field same. Like we identified for the TEMN modes what is the lowest value the indices M or N can take and then it turns out that any one of M or N can take on value 0 and as long as the other one is non-zero the entire field set does not become 0. We will still have sufficient field components remaining to satisfy the Maxwell's equations even if one of M or N index becomes 0 and therefore we identify this fact that the lowest order TE mode is and right now we are not very sure but what we can say is that it is either TE 10 it is not TE 10 it is TE 10 or TE 01 and if you recall the interpretation of these subscripts this would mean that the fields are constant with respect to y the order of variation is 0 and they have the first order of variation along the x direction one maximum between the x equal to 0 to x equal to a conducting volts and similarly one can interpret these two indices alright. With this observation now we are ready to consider the properties which are common to both transverse magnetic and transverse electric modes. Let us go on to do that next TEM and TMM modes and what about the TEM mode transverse electric and magnetic mode? We identified very clearly that for the cylindrical wave guides that we are considering or the hollow metal wave guides that we are considering the transverse electric and magnetic mode cannot be supported. In fact that becomes the distinguishing feature between the transmission lines and the other wave guides in general. We say that a structure which can support a transverse electric and magnetic mode of wave propagation is a transmission line and structures which do not support this are called wave guides although all structures that we have been considering will support propagating waves but we say that the transmission lines support TEM mode of propagation and wave guides do not. Here we have considered one particular type of wave guides the cylindrical wave guides or the hollow metal wave guides. There are possibilities for other types of wave guides as well for example dielectric slab or dielectric rod. In fact an optical fiber is also a wave guide operating at very high frequencies. All these other wave guides other than transmission lines do not support TEM mode of propagation. So that becomes a distinguishing feature between transmission lines and other wave guiding structures. And now let us see what is the significance of this observation or what are the properties associated with non TEM that is TE or TM modes. For this purpose you would recall that we wrote h squared equal to gamma bar squared plus omega squared mu epsilon on one hand and also in terms of the constants a and b we had h squared equal to a squared plus b squared which was further equal to n pi by b whole squared plus m pi by a whole squared. So in this manner h squared is related to the order of the mode m or n and the wave guide dimensions. The other parameters are the frequency and the constitutive parameters of the medium filling the interior of the wave guide and therefore all these things are coming in into picture and they will decide the propagation constant gamma bar. We write gamma bar equal to h squared minus omega squared mu epsilon and therefore it is m pi by a whole squared plus n pi by b whole squared minus omega squared mu epsilon whole squared. And while in general we said that gamma bar the propagation constant can be complex with real part alpha bar and an imaginary part beta bar in this idealized situation where we have ignored losses in the conducting walls or in the dielectric medium filling the wave guide gamma bar would either be completely real below a certain frequency or it would be completely imaginary above a certain frequency. We will have for frequencies less than what is called the cutoff frequency gamma bar going to alpha bar it will become completely real and the fields instead of propagating will simply decay exponentially as e to the power minus alpha z. Such a wave is also called an evanescent wave after a certain distance along the z direction in this case the fields will become negligible as the meaning of the word evanescent would suggest. However above this cutoff frequency omega greater than omega c will have gamma bar completely imaginary and we will have wave propagation without any attendant attenuation at least in this idealized situation. This is the range of frequencies we are normally interested in. This cutoff frequency can be identified from this expression these expressions we have omega c equal to 1 by square root of mu epsilon and then square root of n pi by a whole squared plus n pi by b whole squared and the square root of this whole quantity or this is the radiant frequency the frequency in hertz can also be written it will be replacing 1 by square root of mu epsilon by the velocity of light in the medium filling the wave guide it will be c by 2 and then we have m by a whole squared plus n by b whole squared and the square root of the quantities involving m and n. So this is the cutoff frequency which is related to the velocity of light in the medium in the interior of the wave guide the order of the modes m and n and the wave guide dimensions. The higher the values of m and n the higher the corresponding cutoff frequency. So from this point of view now one can appreciate the significance of the fact what is the lowest order mode for the T m or the T e modes. We said that T m mode has as its lowest order T m 1 1 mode and then in the T e modes we had T e 0 1 as a possibility and also T e 1 0 as the other possibility. For T m 1 1 the cutoff frequency will be given by m equal to 1 and n equal to 1. So for a given wave guide the cutoff frequency of this which we may write as f c 1 1 as far as the expressions are concerned they are not different for the T m modes or the T e modes. So we just write f c 1 1 which of course is less than the cutoff frequency corresponding to either of these less than or greater than it is greater than. For T e 0 1 mode the cutoff frequency is f c 0 1 and it is equal to c by 2 b quite simply and the corresponding cutoff frequency for the last one f c 1 0 is going to be c by 2 a. Now by convention a is the dimension along the x direction and b is the dimension along the y direction and a is taken to be the greater dimension. You could put it in other words x x 6 is oriented along the wider dimension of the cross section. This is almost a universal convention 1 or 2 or text books may use the convention other way round but normally x is the direction associated with the longer dimension along the cross section. From this following this convention now we can see which of these two last cutoff frequencies is greater and we can easily put this kind of sign. Since a is greater than b this cutoff frequency is greater than this cutoff frequency and therefore we find based on this consideration that it is this mode which has the lowest cutoff frequency. If we are given a waveguide and we start increasing the operating frequency it is this mode which will start propagating first of all and as the frequency continues to increase first this mode may appear will be supported by the waveguide and then other modes may appear progressively. So, from that point of view these other modes which appear later at higher frequencies are called higher order modes and this becomes the dominant mode the lowest order mode which is an observation of considerable significance. We have already mentioned that normally we like the propagation in a structure to be in a single mode because if the signal is propagating in a number of modes and these different modes are going to have different characteristics different field configurations and as we shall see different phase velocities distortion is inevitable. And also the fact that a signal is distributed over a number of modes affects the efficiency of excitation of say the waveguide and also the efficiency of collection of the power for that particular signal. And therefore we will prefer that the waveguide or the structure at hand operates in a single mode and that is possible only for the dominant mode of propagation. So, what is the lowest order mode what is the dominant mode for a particular structure is therefore is a consideration of great significance. The other characteristics of TE and TM modes can now be written down we have the expression for the phase shift constant in the frequency range greater than omega c beta bar equal to omega squared mu epsilon minus m pi by a whole squared minus n pi by b whole squared and of course whole squared. From this expression itself we can make out that the phase shift constant beta is not a linear function of frequency. In fact this is more clear if you write the expression for the phase velocity v p bar which is going to be omega by beta bar which is now a function of omega unlike the situation for the infinite medium where these other terms do not appear and we have beta bar equal to square root of omega squared mu epsilon in that case the phase shift the phase velocity is going to be constant at all frequencies but here the phase velocity is not constant with frequency. This is directly a consequence of the fact that the waveguide is not supporting a TEM mode of propagation. This means that some dispersion is unavoidable if the phase velocity is a function of frequency it is different and different frequencies that is going to lead to dispersion. That precisely is dispersion and therefore some dispersion is inevitable which is again a universal characteristic of TEM and TEM modes and therefore all structures which are not transmission lines. That is why we have been stressing the fact whether a structure supports TEM mode or not. If it is not a TEM mode of propagation then the phase velocity is a function of frequency and dispersion and therefore related distortion is unavoidable. As a result of this dispersion if there is a signal which has frequency content which spreads too widely it is likely to get distorted or else it should be propagated over rather short distances and therefore this will have an effect on the bandwidth of the signal that the waveguide can handle or the distance over which a signal with a certain bandwidth can be propagated. The guide wavelength can also be obtained from here lambda bar which is going to be 2 pi by beta bar and one can make out that just as this is less than omega square mu epsilon whole square root. This is greater than the velocity of light in the medium filling the interior of the waveguide and this also is greater than lambda or lambda naught that will be applicable to the interior of the waveguide. Now there are two things that I like to point out here as far as the waveguide is concerned. First thing is that as compared to transmission lines in a waveguide some dispersion is always present. That one could say is a disadvantage of using waveguides. We listed a number of advantages of waveguides there are certain disadvantages also this is one of those. What could be the other disadvantage that comes from the fact that for the waveguide to be able to propagate signal at a certain frequency it must have certain minimum dimensions. So that the cut off frequency that the lowest order mode that can be supported on the waveguide is less than the frequency of the signal that we want to transmit. The cut off frequency as we have seen for even for the lowest order mode f c 1 0 is equal to c by 2 a. So if you want to transmit let us say signal of frequency 5 gigahertz this dimension must have a certain minimum value which will turn out in centimeters. We shall consider an example and this will become clearer and therefore the waveguides are rather bulky. They are not compact because they must have certain minimum cross sectional dimensions to be able to propagate signal at a given frequency. So these are two disadvantages of the waveguides and novel structures transmission structures have been proposed like stripline and transmission line which at least remove the bulkiness part of the waveguides but at the cost of something else. Also these are not easily mass produced these in large quantities is not very economical. But the other structures which may remove some of these limitations will suffer from some other limitations like lower power handling capability and higher attenuation etcetera. We consider the example of an expand waveguide and see what kind of cut off frequencies the waveguide has. The expand waveguides are used very frequently in laboratories it has dimensions which are 0.9 by 0.4 inches or 2.286 centimeters by 1.016 centimeters. The expression for the cut off frequency has been written earlier. Let me just write down the cut off frequencies for the modes of various orders. For the T10 mode the cut off frequency is 6.55 gigahertz and for transmitting signals which are greater than this frequency this waveguide can be utilized which is certainly quite large compared to a thin coaxial cable. So that supports the statement that waveguides are not very compact. The next mode in the order of increasing cut off frequencies is TE20 mode which has a cut off frequency of 13.1 gigahertz. Then TE10 mode has a cut off frequency which is 14.0 30 TE01 thank you. The TE01 mode has a cut off frequency of 14.78 gigahertz and then if you go to TE11 or TM11 the cut off frequency is 16.14 gigahertz. And as we are interested in single mode of operation over the frequency band over which the waveguide is to be utilized one can see that if we restrict our signals within the frequency range 8 to let us say 12 gigahertz then we will maintain single mode of operation. The other modes will be above cut off the waveguide will not support this which is the X band frequency X band frequency range. So in the lecture today we have considered the field expressions for the TM MN and the TE MN modes. We have considered the characteristics of these modes and we considered the example of an X band waveguide. So this is where we stop this lecture. Thank you.