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Trying to implement floating potential

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These things are never easy.
This commit is contained in:
Jorge Gonzalez 2024-09-27 17:56:03 +02:00
commit c39e9ab3fc
5 changed files with 38 additions and 27 deletions
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1
.gitignore vendored
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@ -1,3 +1,4 @@
plasmaExpansion
*.pyc
*.csv
*.mod

47
plasmaExpansion.f90
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@ -40,7 +40,7 @@ module output
integer, parameter:: dataF_id = 30
integer, parameter:: dataPhi_id = 40
integer, parameter:: dataCum_id = 50
character(len=7), parameter:: formatFloat = 'ES0.4e3'
character(len=7), parameter:: formatFloat = 'ES0.6e3'
character(len=3), parameter:: formatSep = '","'
character(len=7):: formatTime
@ -103,7 +103,7 @@ module output
end subroutine writeOutputF
subroutine writeOutputPhi(t, dt, nr, r, phi, n_e)
subroutine writeOutputPhi(t, dt, nr, r, phi, E, n_e)
use constantParameters, only: eV_to_K
use referenceValues, only: L_ref, phi_ref, t_ref, n_ref
@ -112,6 +112,7 @@ module output
real(dp), intent(in):: dt
real(dp), intent(in):: r(1:nr)
real(dp), intent(in):: phi(1:nr)
real(dp), intent(in):: E(1:nr)
real(dp), intent(in):: n_e(1:nr)
character(:), allocatable:: filename
integer:: i
@ -124,11 +125,12 @@ module output
open(unit=dataPhi_id, file=pathOutput//filename)
write(dataPhi_id, '(A)') "t (s)"
write(dataPhi_id, '('//formatFloat//')') t*dt*t_ref
write(dataPhi_id, '(A,2('//formatSep//',A))') "r (m)","phi (V)","n_e (m^-3)"
write(dataPhi_id, '(A,3('//formatSep//',A))') "r (m)","phi (V)","E (V m^-1)","n_e (m^-3)"
do i = 1, nr
write(dataPhi_id, '('//formatFloat//',2('//formatSep //','//formatFloat//'))') &
write(dataPhi_id, '('//formatFloat//',3('//formatSep //','//formatFloat//'))') &
r(i)*L_ref, &
phi(i)*phi_ref, &
E(i)*phi_ref/L_ref, &
n_e(i)*n_ref
end do
@ -328,7 +330,7 @@ program plasmaExpansion
real(dp), allocatable, dimension(:):: phi, phi_old, E
real(dp):: phiConv
real(dp):: phi0
real(dp):: phi0, phiF, JF
integer:: k
real(dp), allocatable, dimension(:):: fCum_i
@ -352,17 +354,17 @@ program plasmaExpansion
! Set input parameters (remember these have to be in non-dimensional units)
Temp0 = 60.0_dp * eV_to_K / Temp_ref
TempF = 10.0_dp * eV_to_K / Temp_ref
TempF = 60.0_dp * eV_to_K / Temp_ref
n_ecr = 1.0e19_dp * cm3_to_m3 / n_ref
c_s = sqrt(T_to_Z(Temp0) * gam * Temp0)
u_bc0 = sqrt(Temp0)
u_bcF = sqrt(TempF)
n_bc0 = n_ecr / T_to_Z(Temp0)
n_bcF = n_ecr*1.0e-1 / T_to_Z(Temp0)
n_bcF = n_bc0!n_ecr*1.0e-1 / T_to_Z(Temp0)
! Set domain boundaries (non-dimensional units)
r0 = 200.0e-6_dp / L_ref
rf = 1.0e-2_dp / L_ref
rf = 6.0e-3_dp / L_ref
dr = 1.0e3_dp
nr = nint((rf - r0) / dr) + 1
dr = (rf - r0) / float(nr-1)
@ -470,8 +472,9 @@ program plasmaExpansion
! Set boundary values
! phi0 = 0.0_dp / phi_ref ! Dirichlet
! phi(1) = phi0 ! Dirichlet
phi0 = phi(1) ! Neumann
phi(nr) = 0.0_dp ! Dirichlet
phi0 = phi(1) ! Neumann
phiF = 0.0_dp ! Dirichlet
JF = 0.0_dp ! Current at the edge for floating potential
allocate(f0(j0:nv))
f0 = 0.0_dp
@ -481,7 +484,7 @@ program plasmaExpansion
t = 0
call writeOutputRef()
call writeOutputF(t, dt, nr, r, nv, v, f_i_old)
call writeOutputPhi(t, dt, nr, r, phi, n_e)
call writeOutputPhi(t, dt, nr, r, phi, E, n_e)
call writeOutputMom(t, dt, nr, r, n_i, u_i, T_i, Zave)
! Main loop
@ -528,7 +531,7 @@ program plasmaExpansion
end if
n_i(i) = sum(f_i(i,:)*dv)
if (n_i(i) > 0.0_dp) then
if (n_i(i) > 1.0e-10_dp) then
u_i(i) = sum(v(:) *f_i(i,:)*dv) / n_i(i)
E_i(i) = sum(v(:)**2*f_i(i,:)*dv) / n_i(i)
T_i(i) = 2.0_dp*E_i(i) - 2.0_dp*u_i(i)**2
@ -544,7 +547,7 @@ program plasmaExpansion
!$omp end parallel do
! Solve Poission (maximum number of iterations, break if convergence is reached before)
do k = 1, 200
do k = 1, 100
! Store previous value
phi_old = phi
@ -566,20 +569,25 @@ program plasmaExpansion
b = -(Zave*n_i - n_e)
! Apply boundary conditions
! b(1) = phi0 ! Dirichlet
b(nr) = 0.0_dp ! Dirichlet
b(nr) = phiF ! Dirichlet
! Calculate residual
!$omp parallel workshare
Res = -(MATMUL(A, phi_old) - b)
!$omp end parallel workshare
! Res(1) = 0.0_dp ! Dirichlet
Res(nr) = 0.0_dp ! Dirichlet
! Iterate system
call dgtsv(nr, 1, diag_low, diag, diag_high, Res, nr, info)
phi = phi_old + Res
phi0 = phi(1) ! Neumann
phi(nr-10:nr) = phi(nr-11)
phi(1) = phi(2) ! Neumann
phi0 = phi(1) ! Neumann
! phi(nr) = phi(nr-5) ! Dirichlet quasi-floating
! Calculate updated current
JF = Zave(nr)*n_i(nr)*u_i(nr) - n_e(nr)*sqrt(qe*T_i(1)*Temp_ref/9.1e-31_dp)/u_ref
! Iterate floating potential
phiF = phi(nr-5)! + 1.0e-2_dp*JF
! Check if the solution has converged
phiConv = maxval(abs(Res),1)
@ -602,7 +610,6 @@ program plasmaExpansion
E(nr) = - (phi(nr) - phi(nr-1)) / dr ! Dirichlet
! E(nr) = 0.0_dp ! Neumann
! Trick to avoid problems at the sheath
E(nr-5:nr) = 0.0_dp
! Update intermediate f
f_i_old = f_i
@ -644,7 +651,7 @@ program plasmaExpansion
! Write output
if (mod(t,everyOutput) == 0 .or. t == nt) then
call writeOutputF(t, dt, nr, r, nv, v, f_i_old)
call writeOutputPhi(t, dt, nr, r, phi, n_e)
call writeOutputPhi(t, dt, nr, r, phi, E, n_e)
call writeOutputMom(t, dt, nr, r, n_i, u_i, T_i, Zave)
call writeOutputFCum(t, dt, r(rCum_index), nv, v, fCum_i)

3
scripts_python/plotCumF.py
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@ -8,8 +8,9 @@ from scipy.constants import e, k
m_i = 1.9712e-25
paths = ['../quasiNeutral_fullAblation/','../Poisson_fullAblation/']
# paths = ['../quasiNeutral_fullAblation/','../Poisson_fullAblation/']
# paths = ['../quasiNeutral_partialAblation/','../Poisson_partialAblation/']
paths = ['../2024-09-27_17.41.21/']
for path in paths:
filesCum_i = sorted(glob.glob(path+'time_*_fCum_i.csv'))
start = 0

11
scripts_python/plotMom.py
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@ -8,23 +8,24 @@ from scipy.constants import e, k
# paths = ['../quasiNeutral_fullAblation/','../2024-09-26_11.48.04/']
# paths = ['../2024-09-26_12.47.11/']
paths = ['../quasiNeutral_partialAblation/','../2024-09-26_13.58.24/']
# paths = ['../quasiNeutral_partialAblation/','../2024-09-26_13.58.24/']
# path = '../quasiNeutral_fullAblation/'
# path = '../quasiNeutral_partialAblatio/'
paths = ['../2024-09-27_17.41.21/']
for path in paths:
filesPhi = sorted(glob.glob(path+'time_*_phi.csv'))
filesMom_i = sorted(glob.glob(path+'time_*_mom_i.csv'))
start = 0
end = len(filesMom_i)
every = 100
every = 50
fig, ax = plt.subplots(4, sharex='all')
for fileMom_i, filePhi in zip(filesMom_i[start:end+1:every], filesPhi[start:end+1:every]):
time, r, phi, n_e = readPhi.read(filePhi)
time, r, phi, E, n_e = readPhi.read(filePhi)
time, r, n_i, u_i, T_i, Zave = readMom.read(fileMom_i)
ax[0].plot(r, phi, label='t = {:.3f} ns'.format(time*1e9))
# ax[0].plot(r, phi, label='t = {:.3f} ns'.format(time*1e9))
ax[0].plot(r, E, label='t = {:.3f} ns'.format(time*1e9))
ax[1].set_yscale('log')
ax[1].set_ylim([1e14,2e25])
ax[1].plot(r, Zave*n_i)

3
scripts_python/readPhi.py
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@ -8,8 +8,9 @@ def read(filename):
df = pandas.read_csv(filename,skiprows=2)
x = df['r (m)'].to_numpy()
phi = df['phi (V)'].to_numpy()
E = df['E (V m^-1)'].to_numpy()
n_e = df['n_e (m^-3)'].to_numpy()
return time, x, phi, n_e
return time, x, phi, E, n_e