Neutralizer

The equations of beamtracer.neutralizer, declared on the code that implements them and checked by the tests.

NeutralizerChannel

classsource

One neutralizer channel traced in (x, y); see the module docstring.

beam

$$J = \frac{I}{w_b H}, \qquad T_\perp = 2 E \theta^2$$

path fractions

$$f_s = \frac{\sum_k N_k \int F_{s,k}\, ds}{\dot N L}, \qquad \dot N = \frac{I}{e H}$$

relaxation

$$f \leftarrow (1 - \omega)\, f + \omega\, f_\mathrm{traced}, \qquad f \leftarrow f_\mathrm{traced} \text{ in the first iteration}$$

convergence

$$\max_s |f_{\mathrm{traced}, s} - f_s| < \text{tolerance} \quad \text{and the plasma converged}$$

exit

$$F_s^\mathrm{exit} = \frac{I_s(x_\mathrm{exit})}{e \dot N}$$

Assumes

• the channel's section in $(x, y)$, planar per metre of the height $H$; grounded walls at $y = \pm w/2$; the beam of width $w_b$ enters as negative ions, centred
• rms divergence $\theta = \sigma_\perp / v_0$, hence $T_\perp = 2 E \theta^2$; the space charge reduced by the plasma's compensation
• the gas target at the plasma's gas target density, the plasma target at its electron density; the plasma model (wellbalanced) takes the path fractions in place of fractions averaged along the axis
• $\omega$ = relaxation (0.7); at most max_iterations, the last state returned with converged=False and no warning

References

• wellbalanced neutralizer

Built from

• BeamOptics
• ChargeChanging