Microtron Accelerators resonant magnetic field

[Kryptonite-19]

Homework Statement

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

Homework 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

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.

 

[TSny]

Try dividing (7) by (5) and solving for ΔW in terms of W_o, 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.