Equation for beta upper limit author: P B Lloyd, CCFE, Culham Science Centre args : output structure : residual error; constraint value; residual error in physical units; output string; units string Equation for beta upper limit #=# physics #=#=# fbeta_max, beta_max and hence also optional here. Logic change during pre-factoring: err, symbol, units will be assigned only if present. i_beta_component : input integer : switch for beta limit scaling (constraint equation 24):
device.dat):| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(out) | :: | tmp_cc | |||
| real(kind=dp), | intent(out) | :: | tmp_con | |||
| real(kind=dp), | intent(out) | :: | tmp_err | |||
| character(len=1), | intent(out) | :: | tmp_symbol | |||
| character(len=10), | intent(out) | :: | tmp_units |
subroutine constraint_eqn_024(tmp_cc, tmp_con, tmp_err, tmp_symbol, tmp_units)
!! Equation for beta upper limit
!! author: P B Lloyd, CCFE, Culham Science Centre
!! args : output structure : residual error; constraint value;
!! residual error in physical units; output string; units string
!! Equation for beta upper limit
!! #=# physics
!! #=#=# fbeta_max, beta_max
!! and hence also optional here.
!! Logic change during pre-factoring: err, symbol, units will be assigned only if present.
!! i_beta_component : input integer : switch for beta limit scaling (constraint equation 24):<UL>
!! <LI> = 0 apply limit to total beta;
!! <LI> = 1 apply limit to thermal beta;
!! <LI> = 2 apply limit to thermal + neutral beam beta
!! <LI> = 3 apply limit to toroidal beta </UL>
!! istell : input integer : switch for stellarator option (set via <CODE>device.dat</CODE>):<UL>
!! <LI> = 0 use tokamak model;
!! <LI> = 1 use stellarator model</UL>
!! fbeta_max : input real : f-value for beta limit
!! beta_max : input real : allowable beta
!! beta : input real : total plasma beta (calculated if ipedestal =3)
!! beta_fast_alpha : input real : fast alpha beta component
!! beta_beam : input real : neutral beam beta component
!! bt : input real : toroidal field
!! btot : input real : total field
use physics_variables, only: i_beta_component, beta_max, beta, beta_beam, beta_fast_alpha, bt, btot
use stellarator_variables, only: istell
use constraint_variables, only: fbeta_max
implicit none
real(dp), intent(out) :: tmp_cc
real(dp), intent(out) :: tmp_con
real(dp), intent(out) :: tmp_err
character(len=1), intent(out) :: tmp_symbol
character(len=10), intent(out) :: tmp_units
! Include all beta components: relevant for both tokamaks and stellarators
if ((i_beta_component == 0).or.(istell /= 0)) then
tmp_cc = 1.0D0 - fbeta_max * beta_max/beta
tmp_con = beta_max
tmp_err = beta_max - beta / fbeta_max
tmp_symbol = '<'
tmp_units = ''
! Here, the beta limit applies to only the thermal component, not the fast alpha or neutral beam parts
else if (i_beta_component == 1) then
tmp_cc = 1.0D0 - fbeta_max * beta_max/(beta-beta_fast_alpha-beta_beam)
tmp_con = beta_max
tmp_err = beta_max - (beta-beta_fast_alpha-beta_beam) / fbeta_max
tmp_symbol = '<'
tmp_units = ''
! Beta limit applies to thermal + neutral beam: components of the total beta, i.e. excludes alphas
else if (i_beta_component == 2) then
tmp_cc = 1.0D0 - fbeta_max * beta_max/(beta-beta_fast_alpha)
tmp_con = beta_max * (1.0D0 - tmp_cc)
tmp_err = (beta-beta_fast_alpha) * tmp_cc
tmp_symbol = '<'
tmp_units = ''
! Beta limit applies to toroidal beta
else if (i_beta_component == 3) then
tmp_cc = 1.0D0 - fbeta_max * beta_max/(beta*(btot/bt)**2)
tmp_con = beta_max
tmp_err = beta_max - (beta*(btot/bt)**2) / fbeta_max
tmp_symbol = '<'
tmp_units = ''
end if
end subroutine constraint_eqn_024