Steady-state plasma composition examples¶

This notebook evaluates steady-state composition for DT, DD, and D-He3 cases using steady_state_plasma_composition(). All available sigmav_* inputs are populated for each case.

In [ ]:

import numpy as np

from fusdb.relations.plasma_composition.plasma_composition import steady_state_plasma_composition
from fusdb.relations.reactions.DD import sigmav_DDn_BoschHale, sigmav_DDp_BoschHale
from fusdb.relations.reactions.DHe3 import sigmav_DHe3_BoschHale
from fusdb.relations.reactions.DT import sigmav_DT_BoschHale
from fusdb.relations.reactions.He3He3 import sigmav_He3He3_CF88
from fusdb.relations.reactions.THe3 import sigmav_THe3_D_CF88, sigmav_THe3_np_CF88
from fusdb.relations.reactions.TT import sigmav_TT_CF88

import numpy as np from fusdb.relations.plasma_composition.plasma_composition import steady_state_plasma_composition from fusdb.relations.reactions.DD import sigmav_DDn_BoschHale, sigmav_DDp_BoschHale from fusdb.relations.reactions.DHe3 import sigmav_DHe3_BoschHale from fusdb.relations.reactions.DT import sigmav_DT_BoschHale from fusdb.relations.reactions.He3He3 import sigmav_He3He3_CF88 from fusdb.relations.reactions.THe3 import sigmav_THe3_D_CF88, sigmav_THe3_np_CF88 from fusdb.relations.reactions.TT import sigmav_TT_CF88

/home/alessmor/Scrivania/fusdb/src/fusdb/relation_util.py:301: RuntimeWarning: Could not convert relation 'Bremsstrahlung radiation' to sympy expression for target 'P_brem'. direct=ValueError: Cannot integrate bremsstrahlung profile over volume.; proxy=ValueError: Cannot integrate bremsstrahlung profile over volume.
  expr, symbols = build_symbolic_model(

In [2]:

constant_profile = np.full(51, 1, dtype=float)

constant_profile = np.full(51, 1, dtype=float)

DT case¶

In [ ]:

T_i_DT = 14 * constant_profile# keV
tau_DT = 1 # s
n_i_DT = 1e20 * constant_profile # m^-3

steady_state_DT = steady_state_plasma_composition(
        n_D = 0.5 * n_i_DT,
        n_T = 0.5 * n_i_DT,
        n_He3 = 0.0 * n_i_DT,
        n_He4 = 0.0 * n_i_DT,
        sigmav_DT = sigmav_DT_BoschHale(T_i=T_i_DT),
        sigmav_DDn = sigmav_DDn_BoschHale(T_i=T_i_DT),
        sigmav_DDp =  sigmav_DDp_BoschHale(T_i=T_i_DT),
        sigmav_DHe3 = sigmav_DHe3_BoschHale(T_i=T_i_DT),
        sigmav_TT = sigmav_TT_CF88(T_i=T_i_DT),
        sigmav_He3He3 = sigmav_He3He3_CF88(T_i=T_i_DT),
        sigmav_THe3_D = sigmav_THe3_D_CF88(T_i=T_i_DT),
        sigmav_THe3_np = sigmav_THe3_np_CF88(T_i=T_i_DT),
        tau_p_D = tau_DT,
        tau_p_T = tau_DT,
        tau_p_He3 = tau_DT,
        tau_p_He4 = tau_DT,  
    )

n_D_DT, n_T_DT, n_He3_DT, n_He4_DT = steady_state_DT
total_density = n_D_DT + n_T_DT + n_He3_DT + n_He4_DT
f_T_avg_DT = np.mean(n_T_DT / total_density)
f_D_avg_DT = np.mean(n_D_DT / total_density)
f_He3_avg_DT = np.mean(n_He3_DT / total_density)
f_He4_avg_DT = np.mean(n_He4_DT / total_density)

print(f"Final DT density fractions:\nf_T_avg = {f_T_avg_DT:.3e}\nf_D_avg = {f_D_avg_DT:.3e}\nf_He3_avg = {f_He3_avg_DT:.3e}\nf_He4_avg = {f_He4_avg_DT:.3e}")
print(f"residual = {1-f_T_avg_DT-f_D_avg_DT-f_He3_avg_DT-f_He4_avg_DT}")

T_i_DT = 14 * constant_profile# keV tau_DT = 1 # s n_i_DT = 1e20 * constant_profile # m^-3 steady_state_DT = steady_state_plasma_composition( n_D = 0.5 * n_i_DT, n_T = 0.5 * n_i_DT, n_He3 = 0.0 * n_i_DT, n_He4 = 0.0 * n_i_DT, sigmav_DT = sigmav_DT_BoschHale(T_i=T_i_DT), sigmav_DDn = sigmav_DDn_BoschHale(T_i=T_i_DT), sigmav_DDp = sigmav_DDp_BoschHale(T_i=T_i_DT), sigmav_DHe3 = sigmav_DHe3_BoschHale(T_i=T_i_DT), sigmav_TT = sigmav_TT_CF88(T_i=T_i_DT), sigmav_He3He3 = sigmav_He3He3_CF88(T_i=T_i_DT), sigmav_THe3_D = sigmav_THe3_D_CF88(T_i=T_i_DT), sigmav_THe3_np = sigmav_THe3_np_CF88(T_i=T_i_DT), tau_p_D = tau_DT, tau_p_T = tau_DT, tau_p_He3 = tau_DT, tau_p_He4 = tau_DT, ) n_D_DT, n_T_DT, n_He3_DT, n_He4_DT = steady_state_DT total_density = n_D_DT + n_T_DT + n_He3_DT + n_He4_DT f_T_avg_DT = np.mean(n_T_DT / total_density) f_D_avg_DT = np.mean(n_D_DT / total_density) f_He3_avg_DT = np.mean(n_He3_DT / total_density) f_He4_avg_DT = np.mean(n_He4_DT / total_density) print(f"Final DT density fractions:\nf_T_avg = {f_T_avg_DT:.3e}\nf_D_avg = {f_D_avg_DT:.3e}\nf_He3_avg = {f_He3_avg_DT:.3e}\nf_He4_avg = {f_He4_avg_DT:.3e}") print(f"residual = {1-f_T_avg_DT-f_D_avg_DT-f_He3_avg_DT-f_He4_avg_DT}")

DD case¶

In [ ]:

T_i_DD = 14 * constant_profile# keV
tau_DD = 1 # s
n_i_DD = 1e20 * constant_profile # m^-3

steady_state_DD = steady_state_plasma_composition(
        n_D = 1 * n_i_DD,
        n_T = 0.0 * n_i_DD,
        n_He3 = 0.0 * n_i_DD,
        n_He4 = 0.0 * n_i_DD,
        sigmav_DT = sigmav_DT_BoschHale(T_i=T_i_DD),
        sigmav_DDn = sigmav_DDn_BoschHale(T_i=T_i_DD),
        sigmav_DDp =  sigmav_DDp_BoschHale(T_i=T_i_DD),
        sigmav_DHe3 = sigmav_DHe3_BoschHale(T_i=T_i_DD),
        sigmav_TT = sigmav_TT_CF88(T_i=T_i_DD),
        sigmav_He3He3 = sigmav_He3He3_CF88(T_i=T_i_DD),
        sigmav_THe3_D = sigmav_THe3_D_CF88(T_i=T_i_DD),
        sigmav_THe3_np = sigmav_THe3_np_CF88(T_i=T_i_DD),
        tau_p_D = tau_DD,
        tau_p_T = tau_DD,
        tau_p_He3 = tau_DD,
        tau_p_He4 = tau_DD,  
    )

n_D_DD, n_T_DD, n_He3_DD, n_He4_DD = steady_state_DD
total_density = n_D_DD + n_T_DD + n_He3_DD + n_He4_DD
f_T_avg_DD = np.mean(n_T_DD / total_density)
f_D_avg_DD = np.mean(n_D_DD / total_density)
f_He3_avg_DD = np.mean(n_He3_DD / total_density)
f_He4_avg_DD = np.mean(n_He4_DD / total_density)

print(f"Final DD density fractions:\nf_T_avg = {f_T_avg_DD:.3e}\nf_D_avg = {f_D_avg_DD:.3e}\nf_He3_avg = {f_He3_avg_DD:.3e}\nf_He4_avg = {f_He4_avg_DD:.3e}")
print(f"residual = {1-f_T_avg_DD-f_D_avg_DD-f_He3_avg_DD-f_He4_avg_DD}")

T_i_DD = 14 * constant_profile# keV tau_DD = 1 # s n_i_DD = 1e20 * constant_profile # m^-3 steady_state_DD = steady_state_plasma_composition( n_D = 1 * n_i_DD, n_T = 0.0 * n_i_DD, n_He3 = 0.0 * n_i_DD, n_He4 = 0.0 * n_i_DD, sigmav_DT = sigmav_DT_BoschHale(T_i=T_i_DD), sigmav_DDn = sigmav_DDn_BoschHale(T_i=T_i_DD), sigmav_DDp = sigmav_DDp_BoschHale(T_i=T_i_DD), sigmav_DHe3 = sigmav_DHe3_BoschHale(T_i=T_i_DD), sigmav_TT = sigmav_TT_CF88(T_i=T_i_DD), sigmav_He3He3 = sigmav_He3He3_CF88(T_i=T_i_DD), sigmav_THe3_D = sigmav_THe3_D_CF88(T_i=T_i_DD), sigmav_THe3_np = sigmav_THe3_np_CF88(T_i=T_i_DD), tau_p_D = tau_DD, tau_p_T = tau_DD, tau_p_He3 = tau_DD, tau_p_He4 = tau_DD, ) n_D_DD, n_T_DD, n_He3_DD, n_He4_DD = steady_state_DD total_density = n_D_DD + n_T_DD + n_He3_DD + n_He4_DD f_T_avg_DD = np.mean(n_T_DD / total_density) f_D_avg_DD = np.mean(n_D_DD / total_density) f_He3_avg_DD = np.mean(n_He3_DD / total_density) f_He4_avg_DD = np.mean(n_He4_DD / total_density) print(f"Final DD density fractions:\nf_T_avg = {f_T_avg_DD:.3e}\nf_D_avg = {f_D_avg_DD:.3e}\nf_He3_avg = {f_He3_avg_DD:.3e}\nf_He4_avg = {f_He4_avg_DD:.3e}") print(f"residual = {1-f_T_avg_DD-f_D_avg_DD-f_He3_avg_DD-f_He4_avg_DD}")

DHe3 case¶

In [ ]:

T_i_DHe3 = 70 * constant_profile# keV
tau_DHe3 = 1 # s
n_i_DHe3 = 1e20 * constant_profile # m^-3

steady_state_DHe3 = steady_state_plasma_composition(
        n_D = 0.5 * n_i_DHe3,
        n_T = 0.0 * n_i_DHe3,
        n_He3 = 0.5 * n_i_DHe3,
        n_He4 = 0.0 * n_i_DHe3,
        sigmav_DT = sigmav_DT_BoschHale(T_i=T_i_DHe3),
        sigmav_DDn = sigmav_DDn_BoschHale(T_i=T_i_DHe3),
        sigmav_DDp =  sigmav_DDp_BoschHale(T_i=T_i_DHe3),
        sigmav_DHe3 = sigmav_DHe3_BoschHale(T_i=T_i_DHe3),
        sigmav_TT = sigmav_TT_CF88(T_i=T_i_DHe3),
        sigmav_He3He3 = sigmav_He3He3_CF88(T_i=T_i_DHe3),
        sigmav_THe3_D = sigmav_THe3_D_CF88(T_i=T_i_DHe3),
        sigmav_THe3_np = sigmav_THe3_np_CF88(T_i=T_i_DHe3),
        tau_p_D = tau_DHe3,
        tau_p_T = tau_DHe3,
        tau_p_He3 = tau_DHe3,
        tau_p_He4 = tau_DHe3,  
    )

n_D_DHe3, n_T_DHe3, n_He3_DHe3, n_He4_DHe3 = steady_state_DHe3
total_density_DHe3 = n_D_DHe3 + n_T_DHe3 + n_He3_DHe3 + n_He4_DHe3
f_T_avg_DHe3 = np.mean(n_T_DHe3 / total_density_DHe3)
f_D_avg_DHe3 = np.mean(n_D_DHe3 / total_density_DHe3)
f_He3_avg_DHe3 = np.mean(n_He3_DHe3 / total_density_DHe3)
f_He4_avg_DHe3 = np.mean(n_He4_DHe3 / total_density_DHe3)

print(f"Final D-He3 density fractions:\nf_T_avg = {f_T_avg_DHe3:.3e}\nf_D_avg = {f_D_avg_DHe3:.3e}\nf_He3_avg = {f_He3_avg_DHe3:.3e}\nf_He4_avg = {f_He4_avg_DHe3:.3e}")
print(f"residual = {1-f_T_avg_DHe3-f_D_avg_DHe3-f_He3_avg_DHe3-f_He4_avg_DHe3}")

T_i_DHe3 = 70 * constant_profile# keV tau_DHe3 = 1 # s n_i_DHe3 = 1e20 * constant_profile # m^-3 steady_state_DHe3 = steady_state_plasma_composition( n_D = 0.5 * n_i_DHe3, n_T = 0.0 * n_i_DHe3, n_He3 = 0.5 * n_i_DHe3, n_He4 = 0.0 * n_i_DHe3, sigmav_DT = sigmav_DT_BoschHale(T_i=T_i_DHe3), sigmav_DDn = sigmav_DDn_BoschHale(T_i=T_i_DHe3), sigmav_DDp = sigmav_DDp_BoschHale(T_i=T_i_DHe3), sigmav_DHe3 = sigmav_DHe3_BoschHale(T_i=T_i_DHe3), sigmav_TT = sigmav_TT_CF88(T_i=T_i_DHe3), sigmav_He3He3 = sigmav_He3He3_CF88(T_i=T_i_DHe3), sigmav_THe3_D = sigmav_THe3_D_CF88(T_i=T_i_DHe3), sigmav_THe3_np = sigmav_THe3_np_CF88(T_i=T_i_DHe3), tau_p_D = tau_DHe3, tau_p_T = tau_DHe3, tau_p_He3 = tau_DHe3, tau_p_He4 = tau_DHe3, ) n_D_DHe3, n_T_DHe3, n_He3_DHe3, n_He4_DHe3 = steady_state_DHe3 total_density_DHe3 = n_D_DHe3 + n_T_DHe3 + n_He3_DHe3 + n_He4_DHe3 f_T_avg_DHe3 = np.mean(n_T_DHe3 / total_density_DHe3) f_D_avg_DHe3 = np.mean(n_D_DHe3 / total_density_DHe3) f_He3_avg_DHe3 = np.mean(n_He3_DHe3 / total_density_DHe3) f_He4_avg_DHe3 = np.mean(n_He4_DHe3 / total_density_DHe3) print(f"Final D-He3 density fractions:\nf_T_avg = {f_T_avg_DHe3:.3e}\nf_D_avg = {f_D_avg_DHe3:.3e}\nf_He3_avg = {f_He3_avg_DHe3:.3e}\nf_He4_avg = {f_He4_avg_DHe3:.3e}") print(f"residual = {1-f_T_avg_DHe3-f_D_avg_DHe3-f_He3_avg_DHe3-f_He4_avg_DHe3}")