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pyrokinetics.diagnostics.gamma_ball_full

pyrokinetics.diagnostics.gamma_ball_full#

pyrokinetics.diagnostics.gamma_ball_full(dPdrho, theta_PEST, B, gradpar, cvdrift, gds2, vguess=None, sigma0=0.42)[source]#

Ideal-ballooning growth rate finder. This function uses a finite-difference method to calculate the maximum growth rate against the infinite-n ideal ballooning mode. The equation being solved is :math::frac{partial}{partial theta} bigg( g frac{partial X}{partial theta} bigg) + c X - lambda f X = 0, g, f > 0

where :math::g = nabla_{||} gds2 / |B| :math::c = frac{1}{nabla_{||}}  frac{partial p}{partial rho} cvdrift :math::f = frac{gds2}{|B|^3} frac{1}{nabla_{||}}

are needed along a field line to solve the ballooning equation once.

:math::gds2 = frac{partialpsi}{partial rho}^2  |nabla alpha|^2, :math::alpha = phi - q (theta - theta_0) which is the field line bending term

:math::nabla_{||} = hat{b} cdot vec{nabla} theta which is the parallel gradient, :math::cvdrift = frac{partialpsi}{partialrho}^2 (hat{b} times (hat{b} cdot vec{nabla} hat{b})) cdot vec{nabla} alpha which is the curvature drift

Parameters:

  • dPdrho (float) – Gradient of the total plasma pressure w.r.t the radial coordinate rho

  • theta_PEST (ArrayLike) – Vector of grid points in a straight field line theta (PEST coordinates)

  • B (ArrayLike) – The magnetic field strength

  • gradpar (ArrayLike) – Parallel gradient

  • cvdrift (ArrayLike) – Geometric factor in curvature drift

  • gds2 (ArrayLike) – Field line bending term

  • vguess (ArrayLike) – starting guess for the eigenfunction (length in N_theta_PEST -2)

  • sigma0 (float) – starting guess for the eigenvalue (square of the growth rate). Must always be greater than the final value. Choose a large value

Returns:

gam – Ideal ballooning growth rate

Return type:

Float

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