AE-Miller

A repo for calculating the available energy of trapped electrons in Miller tokamaks

Dependencies

This code uses the BAD code ( https://github.com/RalfMackenbach/BAD ). It may readily be installed using

pip install -e.

Please follow instructions on the page.

Main idea

This code calculates the available energy (Æ) of any Miller tokamak (R. L. Miller et al.; Noncircular, finite aspect ratio, local equilibrium model. PoP 1998; https://doi.org/10.1063/1.872666 ).

Use

One can install the code by simply running

pip install -e.

in the main directory.

There are two main functions of this code.

s-α

If one wishes the calculate the Æ in the limit of a large-aspect-ratio tokamak with circular flux-surfaces one can use

calc_AE_salpha(omn,eta,epsilon,q,s_q,alpha,L_ref='major',A=3.0,rho=1.0,int_meth='quad',lam_res=1000,output='AE')

Documentation on the input parameters are provided as docstrings.

Miller geometry

If one wishes to calculate the Æ of any Miller tokamak, one can use

calc_AE(omn,eta,epsilon,q,kappa,delta,dR0dr,s_q,s_kappa,s_delta,alpha,theta_res=1001,L_ref='major',A=3.0,rho=1.0,int_meth='quad',lam_res=1000,plot_precs=False,plot_dist=False,Cr_model='r_eff',output='AE')

Documentation on the input parameters are provided as docstrings.

Important input parameters

Besides the plasma and geometric parameters, we highlight several important parameters.

L_ref sets which length-scale is used as reference length. For major, the major radius will be used and omn = - R0/n dn/dr. For minor, the minor radius will be used and omn = - a/n dn/dr. Furthermore, the expansion parameter rho* is adjusted for minor to rho_* = rho_gyro / a. One needs to explicitely set the aspect ratio A and the normalized flux-surface radius rho = r / a when running with L_ref = 'minor'.

int_meth sets the method by which the integral over pitch angle is performed. quad performs best in almost all cases, so it is recommended to run with this setting. However, if one wishes to investigate the Æ per bounce-well (plot_precs=True or plot_dist=True), one needs to run the code with int_meth='trapz'.

Cr_model sets the model for the correlation length. The r_eff model result in the best correlation with nonlinear heat-fluxes, so this is set as the standard.

output can either be AE or Qe. The latter returns the heat-flux according to the scaling of PRL (2022 Mackenbach), applicable for L_ref='minor'.

theta_res is the number of grid-points in theta used to generate the profiles, lam_res (only used if int_meth='trapz') sets the resolution of the trapezoidal integral over pitch angle.