State-of-the-art stellarator optimization code
This tutorial will walk the user through running the BEAMS3D code and generate the necessary output files for FIDASIM.
Table of Contents
BEAMS3D can calculate the steady-state slowing down distribution, which can be used by FIDASIM to generate synthetic FIDA spectra which are directly comparable to experimental data and thus serve as a valuable tool for validation and physics studies.
To generate the FIDASIM files, the code has to be run with either the -fidasim or -fidasim_cyl flag. The following explanation is based on the BEAMS3D validation paper.
The native distribution function in BEAMS3D is collected as a 6-dimensional array, where the dimensions are: number of beams and beam energies, radial bins (units of toroidal flux), poloidal bins (flux aligned), toroidal bins, parallel velocity bins, and perpendicular velocity bins. The resulting distribution is normalized to the real \([\mathrm{m}^{-3}]\) and phase-space volumes \([(\mathrm{m^3/s^3})^{-1}]\), thus giving units of \([\mathrm{s^3/m^6}]\).
FIDASIM requires the distribution to be given on a cylindrical real-space grid (as opposed to the flux-aligned bins of the BEAMS3D distribution) as well as energy and pitch phase-space coordinates, explicitly in units \([\mathrm{1/cm^3/keV}]\). As such, a conversion both in real and phase space is necessary. The phase space conversion is achieved when running with the -fidasim flag by
where \(e\) is the elementary charge in [C], \(v\) is the total velocity in [m/s] and \(m\) is the mass of the fast ion species in [kg]. This has been implemented in BEAMS3D using nearest-neighbor binning to avoid a memory-intensive interpolation.
Alternatively, the distribution function for FIDASIM can also be collected directly alongside the regular distribution (using the -fidasim_cyl flag), resulting in increased memory usage during simulations but significantly increased precision of the distribution, while not significantly affecting overall run time. There are many grid cells in the cylindrical real-space grid outside the plasma, which have to be allocated in memory but are largely free of any fast ions. This memory inefficiency is the main reason why BEAMS3D usually collects the distribution on a flux-aligned grid. However, for the application in the FIDASIM context the increased accuracy by skipping the renormalization and the independence from conversion to flux coordinates makes this approach attractive. This is especially true for cases where continuous flux coordinates are difficult or impossible to construct, as in cases where magnetic islands are included in the equilibrium.
The additional input namelist in the BEAMS3D namelist file has to contain all relevant information for generating the FIDASIM files. Detailed information on the inputs can be found in the FIDASIM documentation.
&fidasim_inputs_b3d
ab = 1.0
adist = 586.108695237747, 667.7809604002308
ai = 1.0
alpha = -1.6792548743640188
aoffy = 19.48, -18.2
aoffz = 9.102, 0.186
ashape = 1, 1
awidy = 30.0, 30.0
awidz = 40.0, 40.0
axis_nbi = -0.107, -0.99, -0.085
axis_spec(:,1) = 0.63102, 0.43877, -0.63976
axis_spec(:,2) = -0.99542, -0.079458, -0.053215
axis_spec(:,3) = 0.58196, 0.43525, -0.68694
axis_spec(:,4) = -0.9939, -0.095986, -0.054339
beta = 0.08527719127138363
calc_bes = 1
calc_birth = 0
calc_brems = 1
calc_cold = 1
calc_dcx = 1
calc_fida = 1
calc_fida_wght = 1
calc_halo = 1
calc_neutron = 0
calc_npa = 0
calc_npa_wght = 0
calc_pfida = 1
calc_pnpa = 0
comment = 'BEAMS3D Distribution function'
current_fractions = 0.5, 0.3, 0.2
device = 'Test device'
divy = 0.0099, 0.010, 0.012
divz = 0.0099, 0.010, 0.012
einj = 55.0
emax_wght = 65.0
focy = 650.0
focz = 850.0
gamma = 0.0
id = 'Channel 1', 'Channel 2', 'Channel 3', 'Channel 4'
impurity_charge = 5
lambdamax = 669.0
lambdamax_wght = 665.0
lambdamin = 645.0
lambdamin_wght = 647.0
lens(:,1) = -52., 541., 106.
lens(:,2) = 210., 610., 37.
lens(:,3) = -52., 541., 105.
lens(:,4) = 210., 610., 37.
n_birth = 10000
n_dcx = 500000
n_fida = 5000000
n_halo = 50000
n_nbi = 50000
n_npa = 5000000
n_pfida = 50000000
n_pnpa = 50000000
name = 'W7X K21:7'
naperture = 2
nbi_data_source = 'generated'
nchan = 48
ne_wght = 10
nlambda = 1024
nlambda_wght = 10
np_wght = 10
nphi_wght = 8
nx = 90
ny = 90
nz = 60
origin = 33., 669., 34.
pinj = 1.7
radius = 595., 596., 594., 593.
result_dir = '' !for current directory
runid = 'fidasim_runid' !! runID
shape = 1
shot = 999999
sigma_pi = 0.9, 0.9, 0.9, 0.9
spec_data_source = 'matlab'
spot_size = 0.0, 0.0, 0.0, 0.0
src = 104., 1321., 90.
system = 'FIDA system'
tables_file = 'atomic_tables.h5'
time = 1.0
widy = 11.0
widz = 25.0
xmax = 180.0
xmin = 0.0
ymax = 180.0
ymin = -80.0
zmax = 60.0
zmin = -60.0
/
The resulting output files are
These can be directly used to run FIDASIM as outlined in its documentation.
The outputs can be analyzed using the functions included in matlabVMEC, as well as the python interface included in FIDASIM.