/sci/ - Science & Math

>>6527904
>velocity modulation?
that's about as close as anything I've found, thank you anon.

it seems the velocity of the charge in conjunction with the velocity of the wave interact.

the whole thing reminds me of aeroelastic flutter, but with EM instead.

Chu & Jackson have the following for the TWT anylysis
2.1 General Field and Wave Equations.

If the fields are circularly symmetric about the axis and assumed to vary with <span class="math">e^{j\omega t \,- \, \gamma\, z}[/spoiler]

The TE wave is described by:
(1)
<span class="math"> \gamma E_\phi + j\omega\mu \, H_r = 0 [/spoiler]
<span class="math">\frac {1}{r} \frac {\partial}{\partial_r}\, (rE_\phi) + j\omega\mu \, H_r = 0[/spoiler]
<span class="math">\frac {\partial H_z}{\partial_r} + \gamma H_r + j\omega\epsilon \, E_\phi = -J_\phi [/spoiler]

The TM wave is described by:
(2)
<span class="math">\gamma H_\phi - j\omega\epsilon \, E_r = J_r [/spoiler]
<span class="math">\frac {1}{r} \, \frac {\partial}{\partial_r} \, (rH_\phi) - j\omega\epsilon \, E_z = J_z[/spoiler]
<span class="math">\frac {\partial E_z}{\partial_r} + \gamma E_r - j\omega\epsilon \, H_\phi = 0 [/spoiler]

Where:
z is helix axis
r is helix radius
<span class="math">\phi[/spoiler] is angle of helix (thread pitch angle)
<span class="math"> \gamma = \alpha + j\beta [/spoiler] is the propagation constant along the z axis
<span class="math">E_z , E_r , E_\phi [/spoiler] are the electric field components
<span class="math">H_z , H_r , H_\phi [/spoiler] are the magnetic field components
<span class="math">J_z , J_r , J_\phi [/spoiler] are the components of the vector current density