8.2. Beam Attenuation

8.2.1. Single Ray Attenuator

class cherab.core.model.attenuator.singleray.SingleRayAttenuator

Calculates beam attenuation in the single-ray approximation. Attenuation is calculated along the beam axis and extrapolated across the beam.

Parameters:

  • step (double) – Distance between sample points along the beam axis in meters for beam stopping calculation. Defaults to 0.01.

  • clamp_to_zero (bint) – Omptimises beam density calculation. If True, the beam density outside the clamping range is zero. Defaults to False.

  • clamp_sigma (double) – The clamping range as a factor of beam \(\sigma(z)\). Defaults to 5.

  • beam (Beam) – The beam instance to which this attenuator is attached. Defaults to None.

  • plasma (Plasma) – The plasma instance with which this beam interacts. Defaults to None.

  • atomic_data (AtomicData) – The atomic data provider class for this attenuator. Defaults to None.

calculate_attenuation()

Trigger beam attenuation calculation

density(x, y, z)

Returns the beam density at the specified point in beam coordinate space. The beam density is calculated as follows:

\[ \begin{align}\begin{aligned}n(x, y, z) = \frac{R}{2\pi v_0 \sigma_x\sigma_y} exp\left(-\frac{1}{2}\left(\frac{x^2}{\sigma_x^2}+\frac{y^2}{\sigma_y^2}\right)\right)exp\left(-\int_{0}^{z}\frac{S(z')}{v_0}dz'\right),\\\sigma_x = \sqrt{\sigma^2 + (ztg(\alpha_x))^2}\hspace{0.5cm}\sigma_y = \sqrt{\sigma^2 + (ztg(\alpha_y))^2},\end{aligned}\end{align} \]

where \(R=\frac{P}{E}\) is the particle rate of the beam defined as the power of the beam divided by the kinetic energy of the single particle, \(v_0=\sqrt{2E/m}\) is the particle speed, \(\sigma\) is the Gaussian beam deviation at origin, \(\alpha_x\) and \(\alpha_y\) are the beam divergence angles in the x and y dimensions respectively, \(S(z)\) is the composite beam attenuation coefficient due to collisional-radiative interaction with the plasma species:

\[ \begin{align}\begin{aligned}S(z) = \sum_{i=1}^{N}Z_i n_i S_i(E_{int}, n_{i,e}^{(eq)}, T_i),\\n_{i,e}^{(eq)} = \frac{1}{Z_i}\sum_{j=1}^{N}Z_j^2 n_j.\end{aligned}\end{align} \]

Here \(Z_i\) is the charge of the i-th type of plasma ions, \(n_i\) is density of the i-th type of plasma ions, \(N\) is the number of type of plasma ions, \(E_{int}\) is the kinetic energy of the beam atoms in the frame of reference where ions of the i-th type are at rest, \(T_{i}\) is the temperature of ions of the i-th type.

The values of partial beam attenuation coefficients, \(S_i\), are provided by the atomic data source.

Parameters:

  • x – x coordinate in meters.

  • y – y coordinate in meters.

  • z – z coordinate in meters.

Returns:

Density in m^-3.