# Microtron Accelerators resonant magnetic field

1. Nov 4, 2013

### Kryptonite-19

1. The problem statement, all variables and given/known data

Somehow combining equations 5 and 7 yields the resonant magnetic field (eqn 8)
and accelerating voltage V (eqn 8a). How is this derived?

2. Relevant equations
eqn5 $$2\,{\frac {\pi \,\Delta W}{eB{C}^{2}}}=b\tau$$

eqn7 $$2\,{\frac {\pi \, \left( w_{{o}}+\Delta W \right) }{eB{c}^{2}}}=a\tau$$

eqn8 $$B=2\,{\frac {\pi \,m_{{o}}c}{e \left( a-b \right) \tau}}$$

eqn8a $$V={\frac {\Delta W}{e}}$$

see also journal page 10 (pdf page2) of http://www.cap.ca/wyp/profiles/Redhead-Jan03.pdf

3. The attempt at a solution

I tried solving eqns 5 and 7 for Tau and got nowhere. Also can't see how the voltage term in eqn 8a appears from combining eqn5 and eqn7.

2. Nov 4, 2013

### TSny

Try dividing (7) by (5) and solving for ΔW in terms of Wo, a, and b. Then sub result for ΔW back into (5).

The middle expression in (8) appears to be off by a factor of c.

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