Input parameters¶

In this page, we describe some of the most important input parameter for Aurora simulations. Since all Aurora inputs are created in Python, rather than in a low-level language, users are encouraged to browse through the module documentation to get a complete picture; here, we only look at some specific features.

Namelist for ion transport simulations¶

The table below describes the main input parameters to Aurora’s forward model of ion transport. Refer to the following sections for details on spatio-temporal grids, recycling and kinetic profiles specifications.

Parameter	Default	Description
imp	Ca	Atomic symbol of the simulated ion.
main_element	D	Background ion species, usually hydrogen isotopes.
source_rate	1e+21	Flux [particles/s] of simulated ions.
source_type	const	Type of ion source, one of [‘file’,’const’,’step’,’synth_LBO’], see `get_source_time_history()`.
explicit_source_vals	None	2D array for sources on explicit_source_time and explicit_source_rhop grids
explicit_source_time	None	Time grid for explicit source
explicit_source_rhop	None	\(\rho_p\) grid for explicit source
source_width_in	0.0	Inner Gaussian source width, only used if >0. See `get_radial_source()`.
source_width_out	0.0	Outer Gaussian source width, only used if >0. See `get_radial_source()`.
imp_source_energy_eV	3.0	Energy of neutral ion source, only used if source_width_in=source_width_out=0, see `get_radial_source()`.
prompt_redep_flag	False	If True, a simple prompt redeposition model is activated, see `get_radial_source()`.
source_file	None	Location of source file, using STRAHL format, only used if source_type=”file”, see `get_source_time_history()`.
source_cm_out_lcfs	1.0	Source distance in cm from LCFS
LBO[“n_particles”]	1e+18	Number of particles in LBO synthetic source, only used if source_type=”synth_LBO”
LBO[“t_fall”]	0.3	Decay time of LBO synthetic source, only used if source_type=”synth_LBO”
LBO[“t_rise”]	0.05	Rise time of LBO synthetic source, only used if source_type=”synth_LBO”
LBO[“t_start”]	0.0	Start time of LBO synthetic source, only used if source_type=”synth_LBO”
timing[“dt_increase”]	[1.005 1. ]	dt multipliers at every time step change. See detailed description.
timing[“dt_start”]	[1.e-05 1.e-03]	dt values at the beginning of each interval/cycle. See detailed description.
timing[“steps_per_cycle”]	[1 1]	Number of steps before dt is multiplied by a dt_increase value. See detailed description.
timing[“times”]	[0. 0.1]	Times at which intervals/cycles change.
bound_sep	2.0	Distance between wall boundary and plasma separatrix [cm].
lim_sep	1.0	Distance between nearest limiter and plasma separatrix [cm].
clen_divertor	17.0	Connection length to the divertor [cm].
clen_limiter	0.5	Connection length to the nearest limiter [cm]
dr_0	0.3	Radial grid spacing on axis. See detailed description.
dr_1	0.05	Radial grid spacing near the wall. See detailed description.
K	6.0	Exponential grid resolution factor. See detailed description.
SOL_decay	0.05	Decay length at the wall bounday, numerical parameter for the last grid point.
saw_model[“saw_flag”]	False	If True, activate sawtooth phenomenological model.
saw_model[“rmix”]	1000.0	Mixing radius of sawtooth model. Each charge state density is flattened inside of this.
saw_model[“times”]	[1.0]	Times at which sawteeth occur.
saw_model[“crash_width”]	1.0	Smoothing width of sawtooth crash [cm].
recycling_flag	False	If True, particles may return to main chamber, either via flows from the SOL or proper recycling.
wall_recycling	0.0	If True, recycling is activated: particles from the wall and divertor may return to main chamber.
source_div_time	None	(Optional) Time base for any particle sources going into the divertor reservoir [s].
source_div_vals	None	(Optional) Particle sources going into the divertor reservoir [particles/s/cm].
tau_div_SOL_ms	50.0	Time scale for transport between the divertor and the open SOL [ms].
tau_pump_ms	500.0	Time scale for pumping out of divertor reservoir [ms].
tau_rcl_ret_ms	50.0	Time scale for retention at the wall [ms] before recycling may occur.
SOL_mach	0.1	Mach number in the SOL, determining parallel loss rates.
kin_profs[“ne”]	{‘fun’: ‘interpa’, ‘times’: [1.0]}	Specification of electron density [\(cm^{-3}\)]. fun=”interpa” interpolates data also in the SOL.
kin_profs[“Te”]	{‘fun’: ‘interp’, ‘times’: [1.0], ‘decay’: [1.0]}	Specification of electron temperature [\(eV\)]. fun=”interp” sets decay over decay length in the SOL.
kin_profs[“Ti”]	{‘fun’: ‘interp’, ‘times’: [1.0], ‘decay’: [1.0]}	Specification of ion temperature [\(eV\)]. Only used for charge exchange rates.
kin_profs[“n0”]	{‘fun’: ‘interpa’, ‘times’: [1.0]}	Specification of background (H-isotope) neutral density [\(cm^{-3}\)].
nbi_cxr	{‘rhop’: None, ‘vals’: None}	Radial profiles of charge exchange rates from NBI neutrals (fast+thermal) for each simulated charge state.
cxr_flag	False	If True, activate charge exchange recombination with background thermal neutrals. Requires kin_profs[“n0”].
nbi_cxr_flag	False	If True, activate charge exchange recombination with NBI neutrals (to be specified in `aurora_sim`).
device	CMOD	Name of experimental device, only used by MDS+ if device database can be read via omfit_eqdsk.
shot	99999	Shot number, only used in combination with device to connect to MDS+ databases.
time	1250	Time [ms] used to read magnetic equilibrium, if this is fetched via MDS+.
acd	None	ADAS ADF11 ACD file (recombination rates). If left to None, uses defaults in `adas_files_dict()` for the chosen ion species.
scd	None	ADAS ADF11 SCD file (ionization rates). If left to None, uses defaults in `adas_files_dict()` for the chosen ion species.
ccd	None	ADAS ADF11 CCD file (nl-unresolved charge exchange rates). If left to None, uses defaults in `adas_files_dict()` for the chosen ion species.

Spatio-temporal grids¶

Aurora’s spatial and temporal grids are defined in the same way as in STRAHL. Refer to the STRAHL manual for details. Note that only STRAHL options that have been useful in the authors’ experience have been included in Aurora.

In short, the create_radial_grid() function produces a radial grid that is equally-spaced on the \(\rho\) grid, defined by

\[\rho = \frac{r}{\Delta r_{centre}} + \frac{r_{edge}}{k+1} \left(\frac{1}{\Delta r_{edge}}- \frac{1}{\Delta r_{centre}} \right) \left(\frac{r}{r_{edge}} \right)^{k+1}\]

The corresponding radial step size is given by

\[\Delta r = \left[\frac{1}{\Delta r_{centre}} + \left(\frac{1}{\Delta r_{edge}} - \frac{1}{\Delta r_{centre}} \right) \left(\frac{r}{r_{edge}}\right)^k \right]^{-1}\]

The radial grid above requires a number of user parameters:

The k factor in the formulae; large values give finer grids at the plasma edge. A value of 6 is usually appropriate.
dr_0 and dr_1 give the radial spacing (in rvol units) at the center and at the last grid point (in cm).

The r_edge parameter in the formulae above is given by:

r_edge = namelist['rvol_lcfs'] + namelist['bound_sep']

where rvol_lcfs is the distance from the center to the separatrix and bound_sep is the distance between the separatrix and the wall boundary, both given in flux-surface-volume normalized units. The rvol_lcfs parameter is automatically computed by the aurora_sim class initialization, based on the provided geqdsk. bound_sep can be estimated via the estimate_boundary_distance() function, if an aeqdsk file can be accessed via MDSplus (alternatively, users may set it to anything they find appropriate). Additionally, since the edge model of Aurora simulates the presence of a limiter somewhere in between the LCFS and the wall boundary, we add a lim_sep parameter to specify the distance between the LCFS and the limiter surface.

To demonstrate the creation of a spatial grid, we are going to select some example parameters:

namelist={}
namelist['K'] = 6.
namelist['dr_0'] = 1.0  # 1 cm spacing near axis
namelist['dr_1'] = 0.1   # 0.1 cm spacing at the edge
namelist['rvol_lcfs'] = 50.0 # 50cm minor radius (in rvol units)
namelist['bound_sep'] = 5.0  # distance between LCFS and wall boundary
namelist['lim_sep'] = 3.0 # distance between LCFS and limiter

# now create grid and plot it
rvol_grid, pro_grid, qpr_grid, prox_param = create_radial_grid(namelist,plot=True)

This will plot the radial spacing over the grid and show the location of the LCFS and the limiter, also specifying the total number of grid points. The larger the number of grid points, the longer simulations will take.

Similarly, to create time grids one needs a dictionary of input parameters, which aurora_sim automatically looks for in the dictionary namelist[‘timing’]. The contents of this dictionary are

timing[‘times’]: list of times at which the time grid must change. The first and last time indicate the start and end times of the simulation.
timing[‘dt_start’]: list of time spacings (dt) at each of the times given by timing[‘times’].
timing[‘steps_per_cycle’]: number of time steps before adapting the time step size. This defines a “cycle”.
timing[‘dt_increase’]: multiplicative factor by which the time spacing (dt) should change within one “cycle”.

Let’s test the creation of a grid and plot the result::

timing = {}
timing['times'] = [0.,0.5, 1.]
timing['dt_start'] = [1e-4,1e-3, 1e-3]  # last value not actually used, except when sawteeth are modelled!
timing['steps_per_cycle'] = [2, 5, 1]   # last value not actually used, except when sawteeth are modelled!
timing['dt_increase'] = [1.005, 1.01, 1.0]  # last value not actually used, except when sawteeth are modelled!
time, save = aurora.create_time_grid(timing, plot=True)

The plot title will show how many time steps are part of the time grid (given by the time output). The save output is a list of 0’s and 1’s that is used to indicate which time grid points should be saved to the output.

Particle sources¶

Core sources of particles can be specified in a number of ways. A time- and radially-dependent source can be set by setting namelist[‘source_type’] = ‘arbitrary_2d_source’ and then providing the parameters

explicit_source_rhop : radial grid (in square root of normalized poloidal flux)
explicit_source_time : time grid (in seconds)
explicit_source_vals : values of source flux (particles/s)

Alternatively, if time and radial dependences of core sources can be effectively separated, source time histories and radial profiles can be described in other ways. The time history of core sources can be created using the get_source_time_history() function, whereas radial profiles of core sources can be defined by specifying parameters for the get_radial_source() function. Please refer to the documentation of these functions for explanations of how to call these.

Particle sources can also be specified such that they enter the simulation from the divertor reservoir. This parameter can be useful to simulate divertor puffing. Note that it can only have an effect if recycling_flag = True and wall_recycling is >=0, so that particles from the divertor are allowed to flow to the main chamber plasma. In order to specify a source into the divertor, one needs to specify 2 parameters:

source_div_time : time base for the particle source into the divertor;
source_div_vals : values of the particle source into the divertor.

Note that while core sources (e.g. in explicit_source_vals) are in units of \(particles/cm^3\), sources going into the divertor have different units of \(particles/cm/s\) since they are going into a 0D edge model.

Edge parameters¶

A 1.5D transport model such as Aurora cannot accurately model edge transport. Aurora uses a number of parameters to approximate the transport of impurities outside of the LCFS; we recommend that users ensure that their core results don’t depend sensitively on these parameters:

recycling_flag: if this is False, no recycling nor communication between the divertor and core plasma particle reservoirs is allowed.
wall_recycling : if this is 0, particles are allowed to move from the divertor reservoir back into the core plasma, based on the tau_div_SOL_ms and tau_pump_ms parameters, but no recycling from the wall is enabled. If >0 and <=1, recycling of particles hitting the limiter and wall reservoirs is enabled, with a recycling coefficient equal to this value.
tau_div_SOL_ms : time scale with which particles travel from the divertor into the SOL, entering again the core plasma reservoir. Default is 50 ms.
tau_pump_ms : time scale with which particles are completely removed from the simulation via a pumping mechanism in the divertor. Default is 500 ms (very long)
tau_rcl_ret_ms : time scale of recycling retention at the wall. This parameter is not present in STRAHL. It is introduced to reproduce the physical observation that after an ELM recycling impurities may return to the plasma over a finite time scale. Default is 50 ms.
SOL_mach: Mach number in the SOL. This is used to compute the parallel loss rate, both in the open SOL and in the limiter shadow. Default is 0.1.

The parallel loss rate in the open SOL and limiter shadow also depends on the local connection length. This is approximated by two parameters: clen_divertor and clen_limiter, in the open SOL and the limiter shadow, respectively. These connection lengths can be approximated using the edge safety factor and the major radius from the geqdsk, making use of the estimate_clen() function.

Kinetic profiles¶

In this section, we add a few more details on the specification of kinetic profiles in the Aurora namelist for 1.5D simulations of ion transport. We reproduce here the rows of the previous table that are relevant to this.

Kinetic profiles specification¶
Parameter	Default	Description
kin_profs[“ne”]	{‘fun’: ‘interpa’, ‘times’: [1.0]}	Specification of electron density [\(cm^{-3}\)]. fun=interpa interpolates data also in the SOL.
kin_profs[“Te”]	{‘fun’: ‘interp’, ‘times’: [1.0], ‘decay’: [1.0]}	Specification of electron temperature [\(eV\)]. fun=interp sets decay over decay length in the SOL.
kin_profs[“Ti”]	{‘fun’: ‘interp’, ‘times’: [1.0], ‘decay’: [1.0]}	Specification of ion temperature [\(eV\)]. Only used for charge exchange rates.
kin_profs[“n0”]	{‘fun’: ‘interpa’, ‘times’: [1.0]}	Specification of background (H-isotope) neutral density [\(cm^{-3}\)].

Simulations that don’t include charge exchange will only need electron density (ne) and temperature (Te). If charge exchange is added, then an ion temperature Ti and background H-isotope neutral density must be specified. Note that Ti should strictly be \(T_{red}=(m_H T_n + m_{imp} T_i)/(T_n+T_i)\), where m_H is the background species mass and T_n is the background neutral temperature, since only the effective (“reduced”) energy of the neutral-impurity interaction enters the evaluation of charge exchange rates. Ti is also used to compute parallel loss rates in the SOL; if not provided by users, it is substituted by Te.

Each field of kin_profs requires specification of fun, times, rhop and vals.

fun corresponds to a specification of interpolation functions in Aurora. Users should choose whether to interpolate data as given also in the SOL (fun=interp) or if SOL profiles should be substituted by an exponential decay. In the latter case, a decay scale length (in \(cm\) units) should also be provided as decay.
times is a 1D array of times, in seconds, at which time-dependent profiles are given. If only a single value is given, whatever it may be, profiles are taken to be time independent.
rhop is a 1D array of radial grid values, given as square-root of normalized poloidal flux.
vals is a 2D array of values of the given kinetic quantity. The first dimension is expected to be time, the second radial coordinate.