The question is fairly simple
In the book "Gyrotrons: High-Power Microwave and Millimeter Wave Technology" from M. V. Kartikeyan, Edith Borie, Manfred Thumm, in page 107 a generalization of Busch theorem, for adiabatic compression assuming a non homogenous magnetic field is written as
Rc=sqrt(b)*Re
where b=B0/Bc (where B0 the magnetic field at the interaction axial position, Bc the magnetic field at the cathode) and Rc the cathode radius and Re the beam radius at the interaction position. This relation is also valid for the beam thickness.
My question is: can we use this relation to find the beam radius and the Larmor radius at any axial position, assuming that we have known the magnetic field, the Larmor radius and the beam radius at a predefined axial position? The compression is adiabatic.
> can we use this relation to find the beam radius and the Larmor radius at any axial position
Sure we can. This relation is adiabatic invariant, for adiabatic B field profile, it is correct.
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