ASCOT5 benchmark

ASCOT5 (LGPL-3.0) is the reference for the beam in the plasma: BBNBI5 for the deposition and shine-through, ascot5_main (guiding centres with Monte Carlo Coulomb collisions) for the slowing down. freeofcharge.ascot5 writes freeofcharge’s equilibrium, plasma, wall and beam as a5py inputs, and benchmarks/ascot5/run_ascot5.py runs both ASCOT5 programs on them and stores the results in benchmarks/ascot5/ascot5_results.json. The example ASCOT5 benchmark runs freeofcharge on the same case and plots both.

The case

freeofcharge.ascot5.benchmark_case():

Equilibrium	Solov’ev, R0 = 1.65 m, outboard minor radius 0.5 m, elongation 1.6, 2.5 T, q = 1 on the axis; 129 × 129 grid; wall on psi_n = 1.3
Plasma	D with 1% C (Z_eff = 1.3); n_e = 5e19 m^-3, T_e = T_i = 2.5 keV in the centre, parabolic (exponents 0.5 and 1.5, 5% at the edge)
Beam	2.5 MW of 60 keV D, tangent to R = 1.0 m from R = 3.5 m, along the field; 10 cm wide, 10 mrad divergence; 2000 markers
Shells	20 equal shells of rho = sqrt(psi_n)

What ASCOT5 is given:

• B_2DS: freeofcharge’s psi on its grid and B_phi = F/R; ASCOT5 takes B_R and B_Z from psi with the same signs. psi0 is moved 1e-6 of the flux difference below the axis value, as ASCOT5 stops markers where its spline of psi dips below psi0.
• plasma_1D: the profiles on freeofcharge’s grid, with two points outside rho = 1 at 1 m^-3 (ASCOT5 stops markers beyond its grid; freeofcharge’s densities are zero there). The ion masses are the mass numbers, as in freeofcharge.
• wall_2D: the wall polygon.
• nbi: one injector with one beamlet per freeofcharge marker and no divergence, so BBNBI5 flies along the freeofcharge lines (its divergence is sqrt(2) times a standard deviation).

BBNBI5 injects 50000 markers at each density of a scan (1e19, 2e19, 5e19 m^-3). Of the ions born at 5e19, 1000 drawn at random are slowed down twice, until 2 T_i or 1 keV: following their orbits (adaptive step, wall and 120 s CPU time per marker as end conditions), and without orbits, the markers staying at their birth points and only colliding (fixed step of 5 µs), which is freeofcharge’s local model. With orbits, 20 of the 1000 markers reached the CPU-time limit before thermalising; none was lost to the wall. The moments come from a5py’s getdist_moments on a rho-theta distribution (8 poloidal bins).

Results

ASCOT5 at commit 24be846, built with Homebrew GCC 16 and HDF5 1.14 on macOS, 2 OpenMP threads. Ratios are freeofcharge over ASCOT5.

Quantity	freeofcharge	ASCOT5	ratio	ASCOT5 without orbits	ratio
Shine-through, n_e0 = 1e19 m^-3	23.03%	23.10 ± 0.19%	0.997
Shine-through, 2e19	5.19%	5.13 ± 0.10%	1.012
Shine-through, 5e19	0.085%	0.094 ± 0.014%	0.91
Ions born [1/s]	2.598e20	2.598e20	1.000
Electron heating [MW]	1.216	1.227	0.991	1.171	1.039
Ion heating [MW]	1.282	1.232	1.040	1.304	0.983
Fast ions	1.29e19	1.09e19	1.18	1.13e19	1.14
Fast-ion energy [kJ]	61.0	54.9	1.11	57.2	1.07
Fast-ion current [kA]	156	59	2.66	136	1.15
Driven current, with shielding [kA]	109	37	2.93	93	1.18

The errors are the binomial standard errors of BBNBI5’s 50000 markers. Shell by shell, the deposited power of the two codes differs by at most 4% of its peak (BBNBI5’s noise); the slowing-down profiles of ASCOT5, from 1000 markers in 20 shells, carry a noise of about 10% per shell.

What agrees

• Deposition and shine-through. Both codes use Suzuki’s beam-stopping fit (freeofcharge’s SuzukiStopping equals ASCOT5’s suzuki_sigmav to 1e-10) along the same lines, so they agree within BBNBI5’s Monte Carlo error at all three densities, and the birth profiles agree shell by shell.
• Heating. The totals and the split between electrons and ions agree to 4% with both ASCOT5 runs. ASCOT5 stops at 2 T_i and hands the rest of the energy (118 kW, 5% of the beam) to the thermal plasma; freeofcharge slows down to rest, mostly heating the ions in that last part. The heating moments of ASCOT5 plus that thermalised energy add up to 103% of the birth power, a measure of the accuracy of the moments.

What does not, and why

• Current, with orbits. freeofcharge’s fast-ion current is 2.7 times ASCOT5’s when ASCOT5 follows the orbits, but agrees with ASCOT5 without orbits to 15%. The beam is born with a mean pitch of 0.55; by the zero-orbit-width criterion (pitch squared below 1 - B/B_max on the birth surface) 42% of the ions are born on trapped orbits, which carry almost no parallel current once their bounce motion is averaged, and the passing ones are spread over a wider radius (the ASCOT5 current is flat inside rho = 0.2). freeofcharge keeps each ion’s local pitch on its birth surface, so it overestimates the current of a beam injected this perpendicularly. An orbit average of the pitch (step 5’s first-orbit correction, or level 3) is needed for the current.
• Fast-ion content (14% to 18%). Without orbits the difference stays, so it is in the collision model, not the orbits. freeofcharge uses one Coulomb logarithm, the electrons’ (NRL, 16.0 in the centre), for the electron and the ion drag; ASCOT5 evaluates it per species and velocity (about 17 for the electrons and 20 for the deuterons at the beam speed, estimated from its formula). A larger ion logarithm raises the critical energy by about 15% and with the shorter slowing-down time shortens the time to thermalise by about 16% at the centre, as observed; it also moves heating to the ions, which the 2 T_i cut-off of ASCOT5 hides in the totals. Separate Coulomb logarithms for electrons and ions are the next change to test.
• Central fast-ion density with orbits. ASCOT5’s density is flat inside rho = 0.2 where freeofcharge’s peaks: the orbit widths of 60 keV deuterons (a few cm) are not small next to the central shells.

Reproducing the ASCOT5 side

ASCOT5 is a benchmark, never a dependency of freeofcharge. On macOS with Homebrew (brew install gcc hdf5):

git clone https://github.com/ascot4fusion/ascot5.git && cd ascot5/src
# run make inside src/: the top-level make writes gitver.h twice in parallel
make -j3 bbnbi5 ascot5_main CC=gcc-16 FLAGS="-I/opt/homebrew/include -L/opt/homebrew/lib"
make -j3 libascot.so CC=gcc-16 FLAGS="-I/opt/homebrew/include -L/opt/homebrew/lib -shared"
mkdir -p ../build && mv bbnbi5 ascot5_main libascot.so ../build/

Homebrew’s h5cc wraps Apple’s clang, which has no OpenMP; GCC with the HDF5 flags works. On Linux, make bbnbi5 ascot5_main libascot with h5cc as in ASCOT5’s documentation.

a5py and freeofcharge in one environment; a5py needs NumPy below 2.3 (int() of size-1 arrays) and unyt 3.0 (recursion in unit conversions with unyt 3.2):

python -m venv a5py-venv && . a5py-venv/bin/activate
pip install -e ./ascot5 -e /path/to/freeofcharge "numpy<2.3" "unyt==3.0.3"
OMP_NUM_THREADS=2 python benchmarks/ascot5/run_ascot5.py --ascot5 /path/to/ascot5/build \
    --work /tmp/ascot5-benchmark --slowing-down-markers 1000

On a laptop with 2 threads, BBNBI5 takes 1 to 3 minutes per density, the slowing down with orbits about 25 minutes, without orbits 10 seconds. BBNBI5 seeds its random numbers from the clock, so the shine-through changes from run to run within its error. --reuse keeps the BBNBI5 runs of --work. Then

python examples/ascot5_benchmark.py

prints both tables and plots the profiles.

References

• E. Hirvijoki et al., ASCOT: Solving the kinetic equation of minority particle species in tokamak plasmas, Comput. Phys. Commun. 185, 1310 (2014).
• J. Varje et al., High-performance orbit-following code ASCOT5 for Monte Carlo simulations in fusion plasmas, arXiv:1908.02482 (2019).
• S. Suzuki et al., Attenuation of high-energy neutral hydrogen beams in high-density plasmas, Plasma Phys. Control. Fusion 40, 2097 (1998).