physics_variables Module

number of energy confinement time scaling laws

beam ion mass (amu)

average mass of fuel portion of ions (amu)

average mass of all ions (amu)

current profile index (calculated from q_0 and q if iprofile=1)

density profile index

pressure profile index

Alpha particle production rate per unit volume, from plasma and beams [particles/m3/sec]

Alpha particle production rate per unit volume, just from plasma [particles/m3/sec]

temperature profile index

aspect ratio (iteration variable 1)

multiplier for beam-background fusion calculation

total plasma beta (iteration variable 5) (calculated if stellarator)

fast alpha beta component

allowable beta

allowable lower beta

neutral beam beta component

poloidal beta

normaised total beta

leading coefficient for NB beta fraction

poloidal field (T)

toroidal field on axis (T) (iteration variable 2)

total toroidal + poloidal field (T)

fractional plasma burnup

fractional plasma burnup user input

vertical field at plasma (T)

Destabalisation parameter for iprofile=6 beta limit

coeff. for sawteeth effects on burn V-s requirement

multiplying factor times plasma volume (normally=1)

maximum ratio of conducting wall distance to plasma minor radius for vertical stability (constraint equation 23)

electron density (/m3) (iteration variable 6)

fuel ion density (/m3)

electron-electron coulomb logarithm

ion-electron coulomb logarithm

density limit (/m3) as calculated using various models

thermal alpha density (/m3)

hot beam ion density, variable (/m3)

hot beam ion density from calculation (/m3)

Troyon-like coefficient for beta scaling

density limit (/m3)

total ion density (/m3)

line averaged electron density (/m3)

proton ash density (/m3)

plasma average "n-tau" (seconds/m3)

high Z ion density (/m3)

Max. normalized gradient length in el. density (ipedestal==0 only)

Max. normalized gradient length in el. temperature (ipedestal==0 only)

maximum (eps*beta_poloidal) (constraint equation 6). Note: revised issue #346 "Operation at the tokamak equilibrium poloidal beta-limit in TFTR", 1992 Nucl. Fusion 32 1468

inverse aspect ratio

fraction of plasma current produced by auxiliary current drive

fraction of plasma current produced inductively

fraction of alpha energy to electrons

Fraction of alpha power deposited in plasma. Default of 0.95 taken from https://doi.org/10.1088/0029-5515/39/12/305.

fraction of alpha power to ions

deuterium fuel fraction

fraction of power to the lower divertor in double null configuration (i_single_null = 0 only) (default assumes SN)

factor to convert plasma surface area to first wall area in neutron wall load calculation (iwalld=1)

fraction of Greenwald density to set as pedestal-top density. If <0, pedestal-top density set manually using neped (ipedestal==1). (iteration variable 145)

fraction of Greenwald density to set as separatrix density. If <0, separatrix density set manually using nesep (ipedestal==1). (iteration variable 152)

helium-3 fuel fraction

physics figure of merit (= plasma_currentaspect*sbar, where sbar=1)

Zohm elongation scaling adjustment factor (ishape=2, 3)

F-value for Psep >= Plh + Paux (constraint equation 73)

F-value for minimum pdivt (constraint equation 80)

f-value for the constraint ne(0) > ne(ped) (constraint equation 81) (Iteration variable 154)

tritium fuel fraction

fusion reaction rate, from beams and plasma (reactions/m3/sec)

fusion reaction rate, just from plasma (reactions/m3/sec)

fraction of the plasma current produced by non-inductive means (iteration variable 44)

Ejima coefficient for resistive startup V-s formula

ratio of (fast alpha + neutral beam beta) to thermal beta

H factors for an ignited plasma for each energy confinement time scaling law

H factor on energy confinement times, radiation corrected (iteration variable 10).

Maximum allowed energy confinement time (s)

switch for bootstrap current scaling

• =1 ITER 1989 bootstrap scaling (high R/a only)
• =2 for Nevins et al general scaling
• =3 for Wilson et al numerical scaling
• =4 for Sauter et al scaling
• =5 for Sakai et al scaling
• =6 for ARIES scaling
• =7 for Andrade et al scaling
• =8 for Hoang et al scaling
• =9 for Wong et al scaling
• =10 for Gi-I et al scaling
• =11 for Gi-II et al scaling

switch for beta limit scaling (constraint equation 24)

• =0 apply limit to total beta
• =1 apply limit to thermal beta
• =2 apply limit to thermal + neutral beam beta
• =3 apply limit to toroidal beta

switch for plasma current scaling to use

• =1 Peng analytic fit
• =2 Peng double null divertor scaling (ST)
• =3 simple ITER scaling (k = 2.2, d = 0.6)
• =4 later ITER scaling, a la Uckan
• =5 Todd empirical scaling I
• =6 Todd empirical scaling II
• =7 Connor-Hastie model
• =8 Sauter scaling allowing negative triangularity
• =9 FIESTA ST fit

switch for diamagnetic current scaling

• =0 Do not calculate
• =1 Use original TART scaling
• =2 Use SCENE scaling

switch for density limit to enforce (constraint equation 5)

• =1 old ASDEX
• =2 Borrass model for ITER (I)
• =3 Borrass model for ITER (II)
• =4 JET edge radiation
• =5 JET simplified
• =6 Hugill-Murakami Mq limit
• =7 Greenwald limit

number of divertors (calculated from i_single_null)

switch for fast alpha pressure calculation

• =0 ITER physics rules (Uckan) fit
• =1 Modified fit (D. Ward) - better at high temperature

switch for ignition assumption. Obviously, ignite must be zero if current drive is required. If ignite is 1, any auxiliary power is assumed to be used only during plasma start-up, and is excluded from all steady-state power balance calculations.

• =0 do not assume plasma ignition
• =1 assume ignited (but include auxiliary power in costs)</UL

switch for inverse quadrature in L-mode scaling laws 5 and 9:

• =0 inverse quadrature not used
• =1 inverse quadrature with Neo-Alcator tau-E used

switch for pedestal profiles:

• =0 use original parabolic profiles
• =1 use pedestal profile

switch for Pfirsch-Schlüter current scaling (issue #413):

• =0 Do not calculate
• =1 Use SCENE scaling

electron density of pedestal [m-3] (`ipedestal==1)

electron density at separatrix [m-3] (`ipedestal==1)

critical ballooning parameter value

critical electron density at separatrix [m-3]

plasma resistivity pre-factor

r/a of density pedestal (ipedestal==1)

r/a of temperature pedestal (ipedestal==1)

r/a where the temperature gradient is largest (ipedestal==0)

r/a where the density gradient is largest (ipedestal==0)

temperature profile index beta (`ipedestal==1)

electron temperature of pedestal (keV) (ipedestal==1)

electron temperature at separatrix (keV) (ipedestal==1) calculated if reinke criterion is used (icc=78)

switch for current profile consistency:

• =0 use input values for alphaj, rli, dnbeta
• =1 make these consistent with input q, q_0 values (recommend i_plasma_current=4 with this option)
• =2 use input values for alphaj, rli. Scale dnbeta with aspect ratio (original scaling)
• =3 use input values for alphaj, rli. Scale dnbeta with aspect ratio (Menard scaling)
• =4 use input values for alphaj, dnbeta. Set rli from elongation (Menard scaling)
• =5 use input value for alphaj. Set rli and dnbeta from Menard scaling
• =6 use input values for alphaj, c_beta. Set rli from Menard and dnbeta from Tholerus

switch for radiation loss term usage in power balance (see User Guide):

• =0 total power lost is scaling power plus radiation
• =1 total power lost is scaling power plus core radiation only
• =2 total power lost is scaling power only, with no additional allowance for radiation. This is not recommended for power plant models.

switch for energy confinement time scaling law (see description in tauscl)

tauscl(ipnlaws) : labels describing energy confinement scaling laws:

• ( 1) Neo-Alcator (ohmic)
• ( 2) Mirnov (H-mode)
• ( 3) Merezkhin-Muhkovatov (L-mode)
• ( 4) Shimomura (H-mode)
• ( 5) Kaye-Goldston (L-mode)
• ( 6) ITER 89-P (L-mode)
• ( 7) ITER 89-O (L-mode)
• ( 8) Rebut-Lallia (L-mode)
• ( 9) Goldston (L-mode)
• (10) T10 (L-mode)
• (11) JAERI-88 (L-mode)
• (12) Kaye-Big Complex (L-mode)
• (13) ITER H90-P (H-mode)
• (14) ITER Mix (L-mode)
• (15) Riedel (L-mode)
• (16) Christiansen (L-mode)
• (17) Lackner-Gottardi (L-mode)
• (18) Neo-Kaye (L-mode)
• (19) Riedel (H-mode)
• (20) ITER H90-P amended (H-mode)
• (21) LHD (stellarator)
• (22) Gyro-reduced Bohm (stellarator)
• (23) Lackner-Gottardi (stellarator)
• (24) ITER-93H (H-mode)
• (25) OBSOLETE
• (26) ITER H-97P ELM-free (H-mode)
• (27) ITER H-97P ELMy (H-mode)
• (28) ITER-96P (=ITER-97L) (L-mode)
• (29) Valovic modified ELMy (H-mode)
• (30) Kaye PPPL April 98 (L-mode)
• (31) ITERH-PB98P(y) (H-mode)
• (32) IPB98(y) (H-mode)
• (33) IPB98(y,1) (H-mode)
• (34) IPB98(y,2) (H-mode)
• (35) IPB98(y,3) (H-mode)
• (36) IPB98(y,4) (H-mode)
• (37) ISS95 (stellarator)
• (38) ISS04 (stellarator)
• (39) DS03 (H-mode)
• (40) Murari et al non-power law (H-mode)
• (41) Petty 2008 (H-mode)
• (42) Lang et al. 2012 (H-mode)
• (43) Hubbard 2017 (I-mode) - nominal
• (44) Hubbard 2017 (I-mode) - lower bound
• (45) Hubbard 2017 (I-mode) - upper bound
• (46) NSTX (H-mode; Spherical tokamak)
• (47) NSTX-Petty08 Hybrid (H-mode)
• (48) NSTX gyro-Bohm (Buxton) (H-mode; Spherical tokamak)
• (49) Use input tauee_in

switch for plasma-first wall clearances:

• =0 use 10% of rminor
• =1 use input (scrapli and scraplo)

switch for plasma cross-sectional shape calculation:

• =0 use input kappa, triang to calculate 95% values
• =1 scale qlim, kappa, triang with aspect ratio (ST)
• =2 set kappa to the natural elongation value (Zohm ITER scaling), triang input
• =3 set kappa to the natural elongation value (Zohm ITER scaling), triang95 input
• =4 use input kappa95, triang95 to calculate separatrix values
• =5 use input kappa95, triang95 to calculate separatrix values based on MAST scaling (ST)
• =6 use input kappa, triang to calculate 95% values based on MAST scaling (ST)
• =7 use input kappa95, triang95 to calculate separatrix values based on fit to FIESTA (ST)
• =8 use input kappa, triang to calculate 95% values based on fit to FIESTA (ST)
• =9 set kappa to the natural elongation value, triang input
• =10 set kappa to maximum stable value at a given aspect ratio (2.6<A<3.6)), triang input (#1399)
• =11 set kappa Menard 2016 aspect-ratio-dependent scaling, triang input (#1439)

switch for spherical tokamak (ST) models:

• =0 use conventional aspect ratio models
• =1 use spherical tokamak models

switch for Spherical Tokamak PF models:

• =0 use Peng and Strickler (1986) model
• =1 use conventional aspect ratio model

switch for neutron wall load calculation:

• =1 use scaled plasma surface area
• =2 use first wall area directly

plasma separatrix elongation (calculated if ishape = 1-5, 7 or 9-10)

plasma elongation at 95% surface (calculated if ishape = 0-3, 6, or 8-10)

plasma elongation calculated as xarea/(pi.a^2)

Volume measure of plasma elongation

central electron density (/m3)

central ion density (/m3)

margin to vertical stability

central total plasma pressure (Pa)

Volume averaged plasma pressure (Pa)

branching ratio for DD -> T

Alpha power per volume just from plasma [MW/m3]

Alpha power per volume from plasma and beams [MW/m3]

Alpha power per volume to electrons [MW/m3]

alpha power escaping plasma and reaching first wall (MW)

alpha power per volume to ions (MW/m3)

Alpha power from only the plasma (MW)

Total alpha power from plasma and beams (MW)

alpha power from hot neutral beam ions (MW)

non-alpha charged particle fusion power (MW)

Total charged particle fusion power [MW]

Non-alpha charged particle fusion power per volume [MW/m3]

profile factor (= n-weighted T / average T)

radiation power from inner zone (MW)

total core radiation power per volume (MW/m3)

deuterium-deuterium fusion power (MW)

deuterium-helium3 fusion power (MW)

power to conducted to the divertor region (MW)

power conducted to the lower divertor region (calculated if i_single_null = 0) (MW)

power conducted to the upper divertor region (calculated if i_single_null = 0) (MW)

power conducted to the divertor with most load (calculated if i_single_null = 0) (MW)

Total deuterium-tritium fusion power, from plasma and beams [MW]

Deuterium-tritium fusion power, just from plasma [MW]

radiation power from outer zone (MW)

edge radiation power per volume (MW/m3)

internal plasma V-s

Nominal mean radiation load on inside surface of reactor (MW/m2)

ion/electron equilibration power per volume (MW/m3)

plasma current (A)

Neutron fusion power from just the plasma [MW]

Total neutron fusion power from plasma and beams [MW]

neutron fusion power per volume from beams and plasma (MW/m3)

neutron fusion power per volume just from plasma (MW/m3)

ohmic heating power (MW)

ohmic heating power per volume (MW/m3)

heating power (= transport loss power) (MW) used in confinement time calculation

fusion power (MW)

plasma poloidal perimeter (m)

total radiation power from inside LCFS (MW)

total radiation power per volume (MW/m3)

radiation power from SoL (MW)

Proton production rate [particles/m3/sec]

SOL radiation power (MW) (stellarator only)

synchrotron radiation power per volume (MW/m3)

switch for L-H mode power threshold scaling to use (see pthrmw for list)

L-H mode power threshold (MW) (chosen via ilhthresh, and enforced if constraint equation 15 is on)

L-H power threshold for various scalings (MW)

• =1 ITER 1996 scaling: nominal
• =2 ITER 1996 scaling: upper bound
• =3 ITER 1996 scaling: lower bound
• =4 ITER 1997 scaling: excluding elongation
• =5 ITER 1997 scaling: including elongation
• =6 Martin 2008 scaling: nominal
• =7 Martin 2008 scaling: 95% upper bound
• =8 Martin 2008 scaling: 95% lower bound
• =9 Snipes 2000 scaling: nominal
• =10 Snipes 2000 scaling: upper bound
• =11 Snipes 2000 scaling: lower bound
• =12 Snipes 2000 scaling (closed divertor): nominal
• =13 Snipes 2000 scaling (closed divertor): upper bound
• =14 Snipes 2000 scaling (closed divertor): lower bound
• =15 Hubbard et al. 2012 L-I threshold scaling: nominal
• =16 Hubbard et al. 2012 L-I threshold scaling: lower bound
• =17 Hubbard et al. 2012 L-I threshold scaling: upper bound
• =18 Hubbard et al. 2017 L-I threshold scaling
• =19 Martin 2008 aspect ratio corrected scaling: nominal
• =20 Martin 2008 aspect ratio corrected scaling: 95% upper bound
• =21 Martin 2008 aspect ratio corrected scaling: 95% lower bound

electron transport power (MW)

electron transport power per volume (MW/m3)

ion transport power (MW)

Total transport power from scaling law (MW)

ion transport power per volume (MW/m3)

Safety factor 'near' plasma edge (iteration variable 18) equal to q95 (unless i_plasma_current=2 (ST current scaling), in which case q = mean edge safety factor qbar)

safety factor on axis

safety factor at 95% surface

plasma fuelling rate (nucleus-pairs/s)

tauratio /1.0/ : ratio of He and pellet particle confinement times

lower limit for edge safety factor

cylindrical safety factor

SoL radiation fraction

Radiation fraction total = SoL + LCFS radiation / total power deposited in plasma

thermal alpha density/electron density (iteration variable 109)

Seeded protium density / electron density.

plasma normalised internal inductance (calculated from alphaj if iprofile=1)

plasma inductance (H)

plasma major radius (m) (iteration variable 3)

plasma minor radius (m)

hot beam density / n_e (iteration variable 7)

n_carbon / n_e

fuel burnup rate (reactions/second)

n_highZ / n_e

n_oxygen / n_e

neo-classical correction factor to rplas

plasma resistance (ohm)

plasma current resistive diffusion time (s)

plasma surface area

outboard plasma surface area

shape factor = plasma poloidal perimeter / (2.pi.rminor)

switch for single null / double null plasma:

• =0 for double null
• =1 for single null (diverted side down)

synchrotron wall reflectivity factor

electron energy confinement time (sec)

Input electron energy confinement time (sec) (isc=48 only)

global thermal energy confinement time (sec)

ion energy confinement time (sec)

alpha particle confinement time (sec)

volume averaged electron temperature (keV) (iteration variable 4)

central electron temperature (keV)

density weighted average electron temperature (keV)

volume averaged ion temperature (keV). N.B. calculated from te if tratio > 0.0

central ion temperature (keV)

density weighted average ion temperature (keV)

ion temperature / electron temperature(used to calculate ti if tratio > 0.0

plasma separatrix triangularity (calculated if ishape = 1, 3-5 or 7)

plasma triangularity at 95% surface (calculated if ishape = 0-2, 6, 8 or 9)

plasma volume (m3)

V-s needed during flat-top (heat + burn times) (Wb)

plasma/device midplane vertical shift - single null

internal and external plasma inductance V-s (Wb)

resistive losses in startup V-s (Wb)

total V-s needed (Wb)

average neutron wall load (MW/m2)

mass of fuel used per day (g)

plasma cross-sectional area (m2)

plasma effective charge

mass weighted plasma effective charge