An argument for this inverse transfer taken from is repeated here, which is based on the so-called "realizability condition" on the magnetic helicity Fourier spectrum H ^ ^ k M = A ^ ^ k ∗ ∗ ⋅ ⋅ B ^ ^ k (where B ^ ^ k is the Fourier coefficient at the wavevector k of the magnetic field B , and similarly for A ^ ^ , the star denoting the complex conjugate). The "realizability condition" corresponds to an application of Cauchy-Schwarz inequality, which yields: | H ^ ^ k M | ≤ ≤ 2 E k M | k | , with E k M = 1 2 B ^ ^ k ∗ ∗ ⋅ ⋅ B ^ ^ k the magnetic energy spectrum. To obtain this inequality, the fact that | B ^ ^ k | = | k | | A ^ ^ k ⊥ ⊥ | (with A ^ ^ k ⊥ ⊥ the solenoidal part of the Fourier transformed magnetic vector potential, orthogonal to the wavevector in Fourier space) has been used, since B ^ ^ k = i k × × A ^ ^ k . The factor 2 is not present in the paper since the magnetic helicity is defined there alternatively as 1 2 ∫ ∫ V A ⋅ ⋅ B d V .