How to use RBG-Maxwell
The main purpose of this part is to let users quickly master the use of RBG-Maxwell framework.
RBG-Maxwell 
1、Usage via an example
The following codes demonstrate an example of how to use RBG-Maxwell.
1.1、 Set the initial conditions
- 1、First, we need to invoke the following package：
import warnings
warnings.filterwarnings("ignore")
# specify the system
from RBG_Maxwell.Collision_database.select_system import which_system
plasma_system = 'Fusion_system'
which_system(plasma_system)
from RBG_Maxwell.Collision_database.Fusion_system.collision_type import collision_type_for_all_species
from RBG_Maxwell.Unit_conversion.main import determine_coefficient_for_unit_conversion, unit_conversion
import numpy as np
from RBG_Maxwell.Plasma.main import Plasma
- 2、Then, we need to specify the unit conversion factor：
- Determine the conversion factors for the International System of Units (IS) and the Flexible System of Units (FS) by configuring the spatial grid, velocity, and charge parameters.
# here we use a pure electron system
# give the quantities in SI
# the spatial grid is chosen to be dx=dy=10**(-5) m
dx = dy = 10**(-5)
dz = 1.
# velocity is roughly 5*10**(6) m/s
v = 5*10**6
# charge
Q = 1.6*10**(-19)
# momentum is roughly 10**(-30)kg*10**7m/s
momentum = 10**(-23)
dp = (10**(-25)*10**(-23)*10**(-23))**(1/3)
# the total number of particles are 5*10**(-13)/(1.6*10**(-19))
# put these particles in 71 spatial grids in z direction
# in 201 spatial grids in y direction
# and 100 momentum grids
# in each phase grid we have dn = 21.89755448111554
# the average value of distribution is roughly
dn = 0.2189755448111554
f = dn/(dp**3*dx*dy*dz)
df = f
# time scale
dt = 10**(-13)
# Now find the coefficient
hbar, c, lambdax, epsilon0 = determine_coefficient_for_unit_conversion(df, dx, dp, Q, f, v, dt)
conversion_table = \
unit_conversion('SI_to_LHQCD', coef_J_to_E=lambdax, hbar=hbar, c=c, k=1., epsilon0=epsilon0)
conversion_table_reverse = \
unit_conversion('LHQCD_to_SI', coef_J_to_E=lambdax, hbar=hbar, c=c, k=1., epsilon0=epsilon0)
For a detailed procedure of unit conversion you can refer to Conversion.
- 3、Next, we need to initialize the plasma system：
- The primary dataset comprises the parameters for time-space discretization, grid quantities, particle classification, and collision classification.
- In the present demonstration, a two-dimensional system consisting of pure electron plasma is utilized, and the initial spatial arrangement of the system is depicted in below.
# time step, and spatial infinitesimals
# dt is 10**(-13) s, dx = dy = dz = 10**(-5) m
dt, dx, dy, dz = 10**(-13)*conversion_table['second'], \
10**(-5)*conversion_table['meter'], \
10**(-5)*conversion_table['meter'], \
10**(-5)*conversion_table['meter']
dt_upper_limit = float(10**(-1)*conversion_table['second'])
dt_lower_limit = float(10**(-9)*conversion_table['second'])
# we have only one type of particle e-
num_particle_species = 1
# treat the electron as classical particles
particle_type = np.array([0])
# masses, charges and degenericies are
masses, charges, degeneracy = np.array([9.11*10**(-31)*conversion_table['kilogram']]), \
np.array([-1.6*10**(-19)*conversion_table['Coulomb']]),\
np.array([1.])
# momentum grids
npx, npy, npz = 1, 201, 1
# half_px, half_py, half_pz
# momentum range for x and z direction are not import in this case
half_px, half_py, half_pz = np.array([9.11*10**(-31)*5*10**6*conversion_table['momentum']]), \
np.array([9.11*10**(-31)*5*10**6*conversion_table['momentum']]),\
np.array([9.11*10**(-31)*5*10**6*conversion_table['momentum']])
par_list=[m1**2*c**2, m2**2*c**2, (2*math.pi*hbar)**3, hbar**2*c, d_sigma/(hbar**2)]
dpx, dpy, dpz = 2*half_px/npx, 2*half_py/npy, 2*half_pz/npz
# load the collision matrix
flavor, collision_type, particle_order = collision_type_for_all_species()
expected_collision_type = ['2TO2']
The parameters related to collisions can be found in Collision_database. The program describes in detail how to set up different colliding plasmas. We also set up the quark-gluon plasma system and the fusion system in this program.
- 4、Set parallel calculation parameters for the plasma system：
- Including the number of Monte Carlo particles, the number of regions, the number of GPUs in the regions, etc.
# number of spatial grids
# must be integers and lists
# odd numbers are recomended
# the maximum spatial gird is limited by CUDA, it's about nx*ny*nz~30000 for each card
nx_o, ny_o, nz_o = [1], [251], [111]
# value of the left boundary
# this is the
x_left_bound_o, y_left_bound_o, z_left_bound_o = [-0.5*dx],\
[-125.5*dy],\
[-55.5*dz]
# number samples gives the number of sample points in MC integration
num_samples = 100
# Only specify one spatial region
number_regions = 1
# each spatial should use the full GPU, this number can be fractional if many regions are chosen
# and only one GPU is available
num_gpus_for_each_region = 0.1
# since only one region is specified, this will be empty
sub_region_relations = {'indicator': [[]],\
'position': [[]]}
# if np.ones are used, the boundaries are absorbing boundaries
# if np.zeros are used, it is reflection boundary
# numbers in between is also allowed
boundary_configuration = {}
for i_reg in range(number_regions):
bound_x = np.ones([ny_o[i_reg], nz_o[i_reg]])
bound_y = np.ones([nz_o[i_reg], nx_o[i_reg]])
bound_z = np.ones([nx_o[i_reg], ny_o[i_reg]])
boundary_configuration[i_reg] = (bound_x, bound_y, bound_z)
For details, please refer to Plasma.
- 5、Set the distribution function and boundary conditions of the plasma system
# iniital distribution function
f = {}
for i_reg in range(number_regions):
f[i_reg] = np.zeros([num_momentum_levels, num_particle_species,\
nx_o[i_reg], ny_o[i_reg], nz_o[i_reg], npx, npy, npz])
# The initial velocity of the electrons is 1.87683*10**6 m/s, corresponds to the momentum value
# 9.11*10**(-31)*1.87683*10**6*conversion_table['momentum'] ~ 408.770512.
# The following code specifies the momentum grid index
dpy = 2*half_py/npy
a = 9.11*10**(-31)*1.87683*10**6*conversion_table['momentum']
ipy = [i for i in range(npy) if (-half_py+dpy*(i-0.5))<=a<=(-half_py+dpy*(i+1))][0]
'''
The total number of particles is 5*10**(-13)/(1.6*10**(-19)) ~ 31249999.999999996.
Put these particles in 101 grids, the number density of the particles is
31249999.999999996/(101*dx*dy*dz) ~ 756837.0957070973 -> Delta_N/Delta_V.
The particles only possess the momentum region of size dpx*dpy*dpz,
hence the distribution function at each phase space grid is
756837.0957070973/(dpx*dpy*dpz) ~ 756837.0957070973/(2*half_px/npx*2*half_py/npy*2*half_pz/npz)
~ 1234.63197049
'''
dn_dv = 5*10**(-14)/(1.6*10**(-19))/(101*dx*dy*dz*dpx*dpy*dpz)
f[0][0, 0, 0,9,5:106,0,ipy,0] = dn_dv
# reshape the distribution function in different regions
for i_reg in range(number_regions):
f[i_reg] = f[i_reg].reshape([num_momentum_levels, num_particle_species,\
nx_o[i_reg]*ny_o[i_reg]*nz_o[i_reg]*npx*npy*npz])
'''
We add an external magnetic field of 10 T in the +y direction
'''
BBy = [10*conversion_table['Tesla']*np.ones(nx_o[0]*ny_o[0]*nz_o[0])]
BEx, BEy, BEz, BBx, BBz = [0],[0],[0],[0],[0]
plasma = Plasma(f,par_list, dt, dt_lower_limit, dt_upper_limit,\
nx_o, ny_o, nz_o, dx, dy, dz, boundary_configuration, \
x_left_bound_o, y_left_bound_o, z_left_bound_o, \
int(npx[0]), int(npy[0]), int(npz[0]), half_px, half_py, half_pz,\
masses, charges, sub_region_relations,\
flavor, collision_type, particle_type,\
degeneracy, expected_collision_type,\
num_gpus_for_each_region,\
hbar, c, lambdax, epsilon0, time_stride_back,\
num_samples = 100, drift_order = 2,\
rho_J_method="raw", GPU_ids_for_each_region = ["1"])
1.2、System evolution and results output
- Set the time step and perform the plasma system evolution.
n_step = 10001
number_rho = []
EM = []
charged_rho = []
dis = []
VT= []
DT = []
import time
start_time = time.time()
for i_time in range(n_step):
# if i_time%1000 == 0:
# dis.append(plasma.acquire_values("Distribution"))
plasma.proceed_one_step(i_time, n_step, processes = {'VT':1., 'DT':1., 'CT':0.},\
BEx = BEx, BEy = BEy, BEz = BEz, BBx = BBx, BBy = BBy, BBz = BBz)
if i_time%1000 == 0:
print('Updating the {}-th time step'.format(i_time))
number_rho.append(plasma.acquire_values("number_rho/J"))
charged_rho.append(plasma.acquire_values("Electric rho/J"))
EM.append(plasma.acquire_values('EM fields on current region'))
end_time = time.time()
- Using pictures to show the evolution of the system.
# spatial distribution
import matplotlib.pyplot as plt
xi, yi = np.mgrid[1:252:1,1:112:1]
fig, axes = plt.subplots(ncols=5, nrows=2, figsize = (15,5))
for jj in range(2):
for kk in range(5):
axes[jj,kk].pcolormesh(xi, yi, number_rho[(jj*5+kk+1)][0][0].reshape([nx_o[0],ny_o[0],nz_o[0]])[0])
Users can easily build own plasma system by learning this example.
For more details in the framework, please refer to For more examples, please refer to