$L=\oint \mathrm{ds}=\oint \rho d\theta =\beta \mathrm{cT}.$ 
$\oint d\theta =2\pi .$ 
$\stackrel{\u203e}{B}=\frac{\oint \mathrm{Bds}}{\oint \mathrm{ds}}=\frac{\oint B\rho \hspace{0.5em}d\theta}{\beta \mathrm{cT}}.$ 
$\stackrel{\u203e}{B}=\frac{2\pi}{T}\frac{{m}_{0}}{q}\hspace{0.5em}\gamma \hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\equiv {B}_{c}\hspace{0.5em}\gamma =\frac{{B}_{c}}{\sqrt{1{\beta}^{2}}}.$ 
$\stackrel{\u203e}{B}=\frac{{B}_{c}}{\sqrt{1(R/{R}_{\infty}{)}^{2}}}.$ 
$k=\frac{\rho}{B}\frac{\mathrm{dB}}{d\rho},$ 
$\kappa =\frac{R}{B}\frac{\mathrm{dB}}{\mathrm{dR}}\approx k\hspace{0.5em}\frac{R}{\rho}$ 
$}$

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Energy  $R$  $\beta \gamma $  $\xi $  $1+2{\mathrm{tan}}^{2}\xi $  ${F}^{2}$  ${\nu}_{z}$ 
100 MeV  175 in.  0.47  0 ${}^{\circ}$  0.0  0.30  0.28 
250 MeV  251 in.  0.78  47 ${}^{\circ}$  3.3  0.20  0.24 
505 MeV  311 in.  1.17  72 ${}^{\circ}$  20.0  0.07  0.24 
$\frac{1}{{\gamma}_{t}^{2}}=\frac{{\nu}_{r}^{3}}{R}\sum _{n}\frac{{a}_{n}{}^{2}}{{\nu}_{r}^{2}{n}^{2}}$ 
$\frac{1}{{\gamma}_{t}^{2}}=\frac{1}{{\nu}_{r}^{2}}+\frac{2{a}_{S}{}^{2}}{R}\frac{{\nu}_{r}^{3}}{{\nu}_{r}^{2}{S}^{2}}$ 