Other quantities

While evolving the main unknown quantities of the equation system, DREAM also calculates a number of help quantities such as collision frequencies, Coulomb logarithms, runaway rates etc., which we refer to as “other quantities” (since they are not unknowns). In contrast to most unknowns, these quantities can be directly evaluated, assuming that the unknowns have been calculated. Since these quantities are often useful when analyzing simulation output, DREAM provides options for storing them as well during the calculation.

Due to the large number of quantities available, some of which may occupy significant amounts of memory, the user must select before the simulation which quantities to save to the output and which to discard. By default, no other quantities are stored.

Storing other quantities

To store a set of other quantities during a DREAM simulation, you must specify the names of the quantities to store when setting up the simulation:

ds = DREAMSettings()
...
ds.other.include('fluid/Eceff', 'fluid/Ecfree', 'fluid/Ectot', 'fluid/EDreic')

A list of available quantities can be found further down on this page.

Note

The reason that we require the user to specify the name of the other quantities desired is to reduce the memory consumption during simulations. In particular the kinetic quantities (hottail/... and runaway/...) can occupy a significant amount of memory during long simulations.

Available quantities

Name	Description
expensive/Tcold_radiationFromNuS	Radiated power density predicted by the Hesslow screened nuS model [J s^-1 m^-3]
fluid/conductivity	Electric conductivity in SI, Sauter formula (based on Braams)
fluid/Eceff	Effective critical electric field [V/m]
fluid/Ecfree	Connor-Hastie threshold field (calculated with n=n_free) [V/m]
fluid/Ectot	Connor-Hastie threshold field (calculated with n=n_tot) [V/m]
fluid/EDreic	Dreicer electric field [V/m]
fluid/f_hot_ripple_pmn	Magnetic ripple resonant momentum for f_hot [mc]
fluid/f_re_ripple_pmn	Magnetic ripple resonant momentum for f_re [mc]
fluid/GammaAva	Avalanche growth rate [s^-1]
fluid/gammaCompton	Compton runaway rate to n_re [s^-1 m^-3]
fluid/gammaCompton	Compton runaway rate [s^-1 m^-3]
fluid/gammaDreicer	Dreicer runaway rate [s^-1 m^-3]
fluid/gammaFhot	Electron flux from f_hot to n_re [s^-1 m^-3]
fluid/gammaFhot	Electron flux from f_hot to f_re [s^-1 m^-3]
fluid/gammaHottail	Hottail runaway rate [s^-1 m^-3]
fluid/gammaLCFSLoss	LCFS runaway loss rate (weights * n_re) [s^-1 m^-3]
fluid/gammaTritium	Tritium runaway rate to n_re [s^-1 m^-3]
fluid/gammaTritium	Tritium runaway rate [s^-1 m^-3]
fluid/Lambda_hypres	Hyper-resistive diffusion coefficient Lambda [H]
fluid/lnLambdaC	Coulomb logarithm (relativistic)
fluid/lnLambdaT	Coulomb logarithm (thermal)
fluid/ni_negIonization	Negative ionization term in ion rate equation
fluid/ni_negRecombination	Negative recombination term in ion rate equation
fluid/ni_posIonization	Positive ionization term in ion rate equation
fluid/ni_posRecombination	Positive recombination term in ion rate equation
fluid/nusnuDatPStar	Slowing-down times deflection frequency for electrons, evaluated at pStar
fluid/pCrit	Critical momentum for avalanche, compton and tritium (in units of mc)
fluid/pCritHottail	Critical momentum for hottail (in units of mc)
fluid/pStar	Effective critical momentum in Hesslow theory
fluid/qR0	Safety factor multiplied by major radius R0 [m]
fluid/reioniz_vsigma	Approximated runaway impact ionization cross-section multiplied by the electron speed [m^-1 s^-1]
fluid/ripple_m	Magnetic ripple poloidal mode number
fluid/ripple_m	Magnetic ripple poloidal mode number
fluid/ripple_n	Magnetic ripple toroidal mode number
fluid/ripple_n	Magnetic ripple toroidal mode number
fluid/runawayRate	Total runaway rate, dn_RE / dt [s^-1 m^-3]
fluid/svensson_A	Advection coefficient used in Svensson n_re transport.
fluid/svensson_A	Advection coefficient used in Svensson n_re transport.
fluid/svensson_D	Advection coefficient used in Svensson n_re transport.
fluid/svensson_transport	Transported runaway density [s^-1 m^-3]
fluid/tauEERel	Relativistic electron collision time (4*pi*lnL*n_cold*r^2*c)^-1 [s]
fluid/tauEETh	Thermal electron collision time (tauEERel * [2T/mc^2]^1.5) [s]
fluid/Tcold_binding_energy	Rate of change in potential energy due to ionisation/recombination [J s^-1 m^-3]
fluid/Tcold_fhot_coll	Collisional heating power density by f_hot [J s^-1 m^-3]
fluid/Tcold_fre_coll	Collisional heating power density by f_re [J s^-1 m^-3]
fluid/Tcold_ion_coll	Collisional heating power density by ions [J s^-1 m^-3]
fluid/Tcold_nre_coll	Collisional heating power density by n_re [J s^-1 m^-3]
fluid/Tcold_ohmic	Ohmic heating power density [J s^-1 m^-3]
fluid/Tcold_radiation	Radiated power density [J s^-1 m^-3]
fluid/Tcold_transport	Transported power density [J s^-1 m^-3]
fluid/W_hot	Energy density in f_hot [J m^-3]
fluid/W_re	Energy density in f_re [J m^-3]
fluid/Wcold_Tcold_Ar	Net radial heat advection [m/s]
fluid/Wcold_Tcold_Drr	Net radial heat diffusion [m/s]
fluid/Zeff	Effective charge
hottail/Ap1	Net first momentum advection on hot electron grid [m/s]
hottail/Ap2	Net second momentum advection on hot electron grid [m/s]
hottail/Ar	Net radial advection on hot electron grid [m/s]
hottail/bremsstrahlung_f1	Advection due to bremsstrahlung radiation
hottail/Dpp	Net momentum-momentum diffusion on hot electron grid [m/s]
hottail/Dpx	Net momentum-pitch diffusion on hot electron grid [m/s]
hottail/Drr	Net radial diffusion on hot electron grid [m/s]
hottail/Dxp	Net pitch-momentum diffusion on hot electron grid [m/s]
hottail/Dxx	Net pitch-pitch diffusion on hot electron grid [m/s]
hottail/kinioniz_vsigma	Kinetic ionization cross-section multiplied by the electron speed [m^-1 s^-1]
hottail/lnLambda_ee_f1	Coulomb logarithm for e-e collisions (on p1 flux grid)
hottail/lnLambda_ee_f2	Coulomb logarithm for e-e collisions (on p2 flux grid)
hottail/lnLambda_ei_f1	Coulomb logarithm for e-i collisions (on p1 flux grid)
hottail/lnLambda_ei_f2	Coulomb logarithm for e-i collisions (on p2 flux grid)
hottail/nu_D_f1	Pitch-angle scattering frequency (on p1 flux grid) [s^-1]
hottail/nu_D_f2	Pitch-angle scattering frequency (on p2 flux grid) [s^-1]
hottail/nu_par_f1	Energy scattering frequency (on p1 flux grid) [s^-1]
hottail/nu_par_f2	Energy scattering frequency (on p2 flux grid) [s^-1]
hottail/nu_s_f1	Slowing down frequency (on p1 flux grid) [s^-1]
hottail/nu_s_f2	Slowing down frequency (on p2 flux grid) [s^-1]
hottail/S_ava	Rosenbluth-Putvinski avalanche source term
hottail/S_compton	Compton scattering source term [s^-1 m^-3]
hottail/S_tritium	Tritium decay source term [s^-1 m^-3]
hottail/synchrotron_f1	Advection due to Synchrotron radiation
hottail/synchrotron_f2	Advection due to Synchrotron radiation
hottail/timevaryingb_Ap2	Pitch angle advection due to time-varying B
runaway/Ap1	Net first momentum advection on runaway electron grid [m/s]
runaway/Ap2	Net second momentum advection on runaway electron grid [m/s]
runaway/Ar	Net radial advection on runaway electron grid [m/s]
runaway/bremsstrahlung_f1	Advection due to bremsstrahlung radiation
runaway/Dpp	Net momentum-momentum diffusion on runaway electron grid [m/s]
runaway/Dpx	Net momentum-pitch diffusion on runaway electron grid [m/s]
runaway/Drr	Net radial diffusion on runaway electron grid [m/s]
runaway/Dxp	Net pitch-momentum diffusion on runaway electron grid [m/s]
runaway/Dxx	Net pitch-pitch diffusion on runaway electron grid [m/s]
runaway/kinioniz_vsigma	Kinetic ionization cross-section multiplied by the electron speed [m^-1 s^-1]
runaway/lnLambda_ee_f1	Coulomb logarithm for e-e collisions (on p1 flux grid)
runaway/lnLambda_ee_f2	Coulomb logarithm for e-e collisions (on p2 flux grid)
runaway/lnLambda_ei_f1	Coulomb logarithm for e-i collisions (on p1 flux grid)
runaway/lnLambda_ei_f2	Coulomb logarithm for e-i collisions (on p2 flux grid)
runaway/nu_D_f1	Pitch-angle scattering frequency (on p1 flux grid) [s^-1]
runaway/nu_D_f2	Pitch-angle scattering frequency (on p2 flux grid) [s^-1]
runaway/nu_par_f1	Energy scattering frequency (on p1 flux grid) [s^-1]
runaway/nu_par_f2	Energy scattering frequency (on p2 flux grid) [s^-1]
runaway/nu_s_f1	Slowing down frequency (on p1 flux grid) [s^-1]
runaway/nu_s_f2	Slowing down frequency (on p2 flux grid) [s^-1]
runaway/S_ava	Rosenbluth-Putvinski avalanche source term
runaway/S_compton	Compton scattering source term [s^-1 m^-3]
runaway/S_tritium	Tritium decay source term [s^-1 m^-3]
runaway/synchrotron_f1	Advection due to synchrotron radiation
runaway/synchrotron_f2	Advection due to synchrotron radiation
runaway/timevaryingb_Ap2	Pitch angle advection due to time-varying B
scalar/ablationDrift	Total distance the deposited material gets shifted
scalar/E_mag	Total energy contained in the poloidal magnetic field within the vessel, normalized to R0 [J/m]
scalar/energyloss_f_hot	Rate of energy loss through plasma edge from f_hot transport, normalized to R0 [J s^-1 m^-1]
scalar/energyloss_f_re	Rate of energy loss through plasma edge from f_re transport, normalized to R0 [J s^-1 m^-1]
scalar/energyloss_T_cold	Rate of energy loss through plasma edge from T_cold transport, normalized to R0 [J s^-1 m^-1]
scalar/L_i	Internal inductance for poloidal magnetic energy normalized to R0 [J/A^2 m]
scalar/l_i	Normalized internal inductance for poloidal magnetic energy (2Li/mu0R0)
scalar/L_i_flux	Internal inductance for poloidal flux psi_p, normalized to R0 [J/A^2 m]
scalar/radialloss_f_hot	Rate of particle number loss through plasma edge from f_hot transport, normalized to R0 [s^-1 m^-1]
scalar/radialloss_f_re	Rate of particle number loss through plasma edge from f_re transport, normalized to R0 [s^-1 m^-1]
scalar/radialloss_n_re	Rate of runaway number loss through plasma edge, normalized to R0 [s^-1 m^-1]
scalar/Ypdot	Rate at which the shards’ radius decrease

Groups

Instead of specifying the name of each quantity separately to the method other.include(), it is also possible to specify the name of group of quantities. The predefined groups are listed below.

Name	Included quantities
ripple	fluid/f_hot_ripple_pmn fluid/f_re_ripple_pmn fluid/ripple_m fluid/ripple_n
transport	scalar/energyloss_f_hot scalar/energyloss_f_re scalar/energyloss_T_cold scalar/radialloss_f_hot scalar/radialloss_f_re scalar/radialloss_n_re
nu_s	hottail/nu_s_f1 hottail/nu_s_f2 runaway/nu_s_f1 runaway/nu_s_f2
nu_D	hottail/nu_D_f1 hottail/nu_D_f2 runaway/nu_D_f1 runaway/nu_D_f2
nu_par	hottail/nu_par_f1 hottail/nu_par_f2 runaway/nu_par_f1 runaway/nu_par_f2
lnLambda	hottail/lnLambda_ee_f1 hottail/lnLambda_ee_f2 hottail/lnLambda_ei_f1 hottail/lnLambda_ei_f2 runaway/lnLambda_ee_f1 runaway/lnLambda_ee_f2 runaway/lnLambda_ei_f1 runaway/lnLambda_ei_f2
energy	fluid/Tcold_fhot_coll fluid/Tcold_fre_coll fluid/Tcold_ion_coll fluid/Tcold_ohmic fluid/Tcold_radiation fluid/Tcold_transport fluid/W_hot fluid/W_re scalar/E_mag scalar/energyloss_f_hot scalar/energyloss_f_re scalar/energyloss_T_cold scalar/L_i scalar/l_i

Time grid

The other quantities use almost exactly the same time grid as regular unknowns, with the only difference that other quantities are not defined for \(t=0\). This is due to the fact that many quantities are only/can only be calculated while taking/after the first time step. Consequently, you should remove the first time point in grid.t whenever plotting or working with other quantities.