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velocity_moments

moment_kinetics.velocity_moments.integrate_over_negative_vpa — Method

computes the integral over vpa <= 0 of the integrand, using the input vpa_wgts this could be made more efficient for the case that dz/dt = vpa is time-independent, but it has been left general for the cases where, e.g., dz/dt = wpa*vth + upar varies in time

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moment_kinetics.velocity_moments.integrate_over_positive_vpa — Method

computes the integral over vpa >= 0 of the integrand, using the input vpa_wgts this could be made more efficient for the case that dz/dt = vpa is time-independent, but it has been left general for the cases where, e.g., dz/dt = wpa*vth + upar varies in time

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moment_kinetics.velocity_moments.update_chodura_integral_species! — Method

compute the integral needed for the generalised Chodura condition

IChodura = (Z^2 vBohm^2 / cref^2) * int ( f bz^2 / vz^2 + dfdr*rhostar/vz ) vBohm = sqrt(Z Te/mi) with Z = 1 and mref = mi cref = sqrt(2Ti/mi) and normalise to the local ion density, appropriate to assessing the Chodura condition 

IChodura <= (Te/e)d ne / dphi |(sheath entrance) = ni

to a single species plasma with Z = 1

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moment_kinetics.velocity_moments.update_derived_electron_moment_time_derivatives! — Method

'Primary' time derivatives are calculated when doing the time advance for moment quantities. Moment kinetic equations require in addition some 'derived' time derivatives, which we can calculate by applying the chain rule.

For electrons the kinetic equation that is solved for the shape function is simplified by using $\sqrt{m_e/m_i}$ as a small parameter after substituting in the moment equations. Therefore it is not possible (or at least not convenient) to use dppar_dt as calculated from the moment equation. The electron moment time derivatives may still be useful as diagnostics, so we calculate them anyway, including the derived versions (calculated in this function), similar to the ion moment time derivatives.

Note that due to the implicit/explicit splitting of terms in the timestep, which means that the density (which is equal to the ion density) does not update during the implicit electron timestep, the time derivative of density dn/dt does not contribute to the chain rule calculations in this function, even though analytically it would contribute (although the contribution would be small in sqrt(me/mi)). Another way of saying this is that due to the operator splitting, the time derivatives during the implicit step are done with the explicit variables (density in particular) held fixed, and so dvth_dt|_n = 0.5 * vth * dppar_dt / ppar.

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moment_kinetics.velocity_moments.update_moments! — Method

calculate the updated density (dens) and parallel pressure (ppar) for all species this function is only used once after initialisation the function used to update moments at run time is updatederivedmoments! in time_advance.jl

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