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Documentation
Basics
Geometry
INPUT
INPUT_profiles
Output files
Platform files

Contents

Basics

Input Files

All GYRO input parameters reside in one of two files:

INPUT must always exist, whereas INPUT_profiles is required only when simulations are based on experimental profiles. These files are local to a given simulation directory, or simdir. Both INPUT and INPUT_profiles are parsed by a python script to generate new input files to be read directly by GYRO. The user need not pay attention to python-generated files.

Species Notation

We use the following simplified notation for species indices: \sigma=\left\{e,1,2,\ldots\right\}. Here, e\,\! corresponds to electrons, while {1,2,\ldots} correspond to primary ion, secondary ion, and so on. For example:

Symbol INPUT Parameter Meaning
n_e\,\! (unit) Electron density
n_1\,\! NI_OVER_NE First (main) ion density
n_2\,\! NI_OVER_NE_2 Second ion density
n_3\,\! NI_OVER_NE_3 Third ion density
1/L_{n_e}\,\! DLNNDR_ELECTRON Electron density gradient inv. length
1/L_{n_1}\,\! DLNNDR First (main) ion density gradient inv. length
1/L_{n_2}\,\! DLNNDR_2 Second ion density gradient inv. length
1/L_{n_3}\,\! DLNNDR_3 Third ion density gradient inv. length

Normalization

Lengths and times in GYRO are normalized according to the quantities in the table below. An overbar, in general, means that the quantity is evaluated at the reference radius, {\bar r}\,\!.

Quantity Unit Description
Length a\,\! Minor radius
Velocity {\bar c_s}\,\! Sound speed at reference radius
Time a/{\bar c_s}\,\! Minor radius over sound speed at the reference radius

Diffusivities in GYRO output files are expressed in gyroBohm units.

We have also defined

Reference radius 
{\bar r}\,\! (this is specified using RADIUS).
Ion sound gyroradius 
\rho_{s,{\rm unit}} = \frac{c_s}{e B_{\rm unit}/(m_1 c)}\,\!
Ion sound speed 
c_s=\sqrt{T_e/m_i}\,\!
gyroBohm unit diffusivity 
\chi_{\rm GB} = {\bar\rho}_{s,{\rm unit}}^2 {\bar c_s}/a \,\!

Computed Quantities

In this section we list primitive definitions of computed quantities. The normalization of these quantities is detailed in the output file section.

Potentials

The electrostatic potential is

\delta\phi(r,\theta,\varphi) = \sum_{j=-N_n+1}^{N_n-1}\delta\phi_n(r,\theta) e^{-i n \alpha} , where n = j \Delta n\,\! .

The parallel part of the vector potential is

\delta A_\lVert(r,\theta,\varphi) = \sum_{j=-N_n+1}^{N_n-1}\delta A_{\lVert n}(r,\theta) e^{-i n \alpha} , where n = j \Delta n\,\! .

Above, \alpha = \varphi + \nu(r,\theta)\,\! (see geometry notes for more details).

These expansions are subject to the reality condition \delta\phi_{-n}=\delta\phi_n^*\,\!. Thus, we solve numerically for the coefficients n \ge 0\,\!, and obtain the others by reflection.

Eigenmode frequencies

For linear simulations only, GYRO will compute the mode frequency and growth rate under the assumption that

\delta\phi_n(r,\theta,t) = \widehat{\delta\phi_n}(r,\theta) e^{-i \omega_n t}\,\! ,

such that

\omega_n = \omega_{R,n} + i \gamma_n\,\! .

Density fluctuations

\delta n_\sigma(r,\theta,\varphi) = \int d^3 v \, \delta f_\sigma(\mathbf{x}) = \sum_{j=-N_n+1}^{N_n-1}\delta n_{\sigma,n}(r,\theta) e^{-i n \alpha}

Energy fluctuations

\delta E_\sigma(r,\theta,\varphi) = \int d^3 v \, \frac{m_\sigma v^2}{2} \delta f_\sigma(\mathbf{x}) = \sum_{j=-N_n+1}^{N_n-1}\delta E_{\sigma,n}(r,\theta) e^{-i n \alpha}

Particle diffusivity

For nonlinear simulations, or linear simulations with quasilinear estimates, we define

D_\sigma(r) = - \frac{\Gamma_\sigma}{\partial n_\sigma/\partial r}, where \Gamma_\sigma(r) = \left\langle \int d^3v \, \delta f_\sigma(x) \, \left( \frac{1}{B} \, \mathbf{b} \times\nabla U \right)\cdot \mathbf{r} \right\rangle

is the particle flux. Because D_\sigma\,\! is bilinear, it is computed as a sum over n\,\!

D_\sigma(r) = \sum_{j=1}^{N_n-1} D_{\sigma,n}(r)\,\! where n = j \Delta n\,\! .

Note that there is no contribution from n=0\,\!.

Energy diffusivity

For nonlinear simulations, or linear simulations with quasilinear estimates, we define

\chi_\sigma(r) = - \frac{Q_\sigma}{n_\sigma \partial T_\sigma/\partial r}, where Q_\sigma(r) = \left\langle \int d^3v \, \frac{m_\sigma v^2}{2} \delta f_\sigma(x) \, \left( \frac{1}{B} \, \mathbf{b} \times\nabla U \right)\cdot \mathbf{r} \right\rangle

is the energy flux. Because \chi_\sigma\,\! is bilinear, it is computed as a sum over n\,\!

D_\sigma(r) = \sum_{j=0}^{N_n-1} \chi_{\sigma,n}(r)\,\! where n = j \Delta n\,\! .

Note that there is no contribution from n=0\,\!.

Contributions from magnetic flutter

Note that the diffusivities have so-called electrostatic and magnetic flutter components, corresponding to the \delta\phi\,\! and \delta A_\lVert parts of

U = \delta\phi - \frac{v_\lVert}{c} \delta A_\lVert .
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