Electro-Magnetic Field
This section configures the Electro-Magnetic field settings and is optional. If not present the code will use the default values. It accepts the following data:
- smooth_type, character(*), default = “none”
- smooth_niter, integer, default = 1
- smooth_nmax, integer, default = -1
- type_init_b, character(*), default = “uniform”
- type_init_e, character(*), default = “uniform”
- init_b0(3), float, default = 0.0
- init_e0(3), float, default = 0.0
- init_b_mfunc(3), character(*), default = “NO_FUNCTION_SUPPLIED!”
- init_e_mfunc(3), character(*), default = “NO_FUNCTION_SUPPLIED!”
- init_dipole_b_m(3), real, default = 0.0
- init_dipole_b_x0(1:x_dim), real, default = 0.0
- init_dipole_b_r0, real, default = 0.001
- init_dipole_e_p(3), real, default = 0.0
- init_dipole_e_x0(1:p_x_dim), real, default = 0.0
- init_dipole_e_r0, real, default = 0.001
- ext_fld, character(*), default = “none”
- type_ext_b, character(*), default = “uniform”
- type_ext_e, character(*), default = “uniform”
- ext_b0(3), float, default = 0.0
- ext_e0(3), float, default = 0.0
- ext_b_mfunc(3), character(*), default = “NO_FUNCTION_SUPPLIED!”
- ext_e_mfunc(3), character(*), default = “NO_FUNCTION_SUPPLIED!”
- ext_dipole_b_m(3), real, default = 0.0
- ext_dipole_b_x0(1:x_dim), real, default = 0.0
- ext_dipole_b_r0, real, default = 0.001
- ext_dipole_e_p(3), real, default = 0.0
- ext_dipole_e_x0(1:p_x_dim), real, default = 0.0
- ext_dipole_e_r0, real, default = 0.001
- solver, character(*), default = “yee”
smooth_type controls the type of smoothing to be applied to the EM fields. The actual smoothing parameters are set in a smooth section that must follow this section. It accepts the following options:
- “none” - No smoothing is applied to the EM fields. This is the default.
- “stand” - The EM fields are smoothed only for particle interpolation. The smoothing process will not affect the actual EM fields used in the field solver. Smoothing is applied at every time step.
- “local” - The smoothing is applied to the simulation EM fields. This will affect all EM fields in the simulation and will have a cumulative effect, because the EM fields being smoothed in a given iteration will have already been smoothed previously. See also smooth_niter and smooth_nmax.
- “nci” - Numerical Cherenkonv Instability filter [1]. This is a special filter that is applied in the x1 direction only, and only to fields seen by the particles.
smooth_niter specifies the number of iterations between smooth passes for the “local” smooth. The default is 1, meaning the local smooth will be applied at every time step. smooth_nmax specifies the final iteration at which the “local” smooth will be applied. After this iteration, the smooth type will be set to “none”. The default is -1, meaning the smoothing will not stop.
type_init_b specifies the type of initial field to be used for each component of the magnetic field. Valid values are:
- “uniform” - uniform field (default)
- “math func” - field defined by a user supplied analytical expression. This expression can be a function of the spatial coordinates (x1, x2, and x3).
- “dipole” - dipolar field (not available for 1D simulations).
type_init_e specifies the type of initial field to be used for each component of the electric field. This parameter has the same form as type_init_b.
init_b0 specifies the values for an initial magnetic field of type “uniform”.
init_e0 specifies the values for an initial electric field of type “uniform”.
init_b_mfunc specifies the analytical expression to be used for calculating the initial magnetic field of type “math func”. This expression can be a function of any of the following, which represent the physical coordinates of the position being calculated: x1 (in 1D, 2D and 3D), x2 (in 2D and 3D) and x3 (in 3D). See the documentation on the analytical function parser for details on the mathematical expression.
init_e_mfunc specifies the analytical expression to be used for calculating the initial electric field of type “math func”. This parameter has the same form as ext_b_mfunc.
init_dipole_b_m specifies the magnetic dipole moment of the dipole contributing for an initial magnetic field of type “dipole”. The dipole definition follows the definition given in Jackson, Classical Electrodynamics, 3rd edition, eq. (5.64), Wiley & Sons, 1998. The parameters init_dipole_b_x0 and init_dipole_b_r0 define the remaining parameters for the dipole.
init_dipole_b_x0 specifies the position of the dipole contributing for an external magnetic field of type “dipole”. See the parameters init_dipole_b_m and init_dipole_b_r0 for further details.
init_dipole_b_r0 specifies the minimum distance from the dipole position below which the field contributing for an external magnetic field of type “dipole” is set to the value at the dipole position. See the parameters dipole_b_m and dipole_b_x0 for further details.
init_dipole_e_p specifies the electric dipole moment of the dipole contributing for an initial electric field of type “dipole”. The dipole definition follows the definition given in Jackson, Classical Electrodynamics, 3rd edition, eq. (4.20), Wiley & Sons, 1998. The parameters init_dipole_e_x0 and init_dipole_e_r0 define the remaining parameters for the dipole.
init_dipole_e_x0 specifies the position of the dipole contributing for an initial electric field of type “dipole”. See the parameters init_dipole_e_p and init_dipole_e_r0 for further details.
init_dipole_e_r0 specifies the minimum distance from the dipole position below which the field contributing for an initial electric field of type “dipole” is set to the value at the dipole position. See the parameters init_dipole_e_m and init_dipole_e_x0 for further details.
ext_fld Controls the use of external electrical and magnetic fields in the simulation. Valid options are:
- “none” - Use only the self generated electric and magnetic fields in the simulation. This is the default.
- “static” - Use also an externally supplied electric and/or magnetic field that is constant in time.
- “dynamic” - Same as the previous option, but allows for the external field to vary in time (e.g. used in boosted frame simulations). This will only affect external fields of type “math func”
type_ext_b specifies the type of external field to be used for each component of the magnetic field. Valid values are:
- “uniform” - uniform field (default)
- “math func” - field defined by a user supplied analytical expression. This expression can be a function of the spatial coordinates (x1, x2, and x3) and, if the ext_fld parameter is set to “dynamic”, also of time (t).
- “dipole” - dipolar field (not available for 1D simulations).
type_ext_e specifies the type of external field to be used for each component of the electric field. This parameter has the same form as type_ext_b.
ext_b0 specifies the values for an external magnetic field of type “uniform”.
ext_e0 specifies the values for an external electric field of type “uniform”.
ext_b_mfunc specifies the analytical expression to be used for calculating the external magnetic field of type “math func”. This expression can be a function of any of the following, which represent the physical coordinates of the position being calculated: x1 (in 1D, 2D and 3D), x2 (in 2D and 3D) and x3 (in 3D). For ‘dynamic’ external fields the variable t (time) is also allowed. See the documentation on the analytical function parser for details on the mathematical expression.
ext_e_mfunc specifies the analytical expression to be used for calculating the external electric field of type “math func”. This parameter has the same form as ext_b_mfunc.
ext_dipole_b_m specifies the magnetic dipole moment of the dipole contributing for an external magnetic field of type “dipole”. The dipole definition follows the definition given in Jackson, Classical Electrodynamics, 3rd edition, eq. (5.64), Wiley & Sons, 1998. The parameters ext_dipole_b_x0 and ext_dipole_b_r0 define the remaining parameters for the dipole.
ext_dipole_b_x0 specifies the position of the dipole contributing for an external magnetic field of type “dipole”. See the parameters ext_dipole_b_m and ext_dipole_b_r0 for further details.
ext_dipole_b_r0 specifies the minimum distance from the dipole position below which the field contributing for an external magnetic field of type “dipole” is set to the value at the dipole position. See the parameters dipole_b_m and dipole_b_x0 for further details.
ext_dipole_e_p specifies the electric dipole moment of the dipole contributing for an external electric field of type “dipole”. The dipole definition follows the definition given in Jackson, Classical Electrodynamics, 3rd edition, eq. (4.20), Wiley & Sons, 1998. The parameters dipole_e_x0 and dipole_e_r0 define the remaining parameters for the dipole.
ext_dipole_e_x0 specifies the position of the dipole contributing for an external electric field of type “dipole”. See the parameters ext_dipole_e_p and ext_dipole_e_r0 for further details.
ext_dipole_e_r0 specifies the minimum distance from the dipole position below which the field contributing for an external electric field of type “dipole” is set to the value at the dipole position. See the parameters dipole_e_m and dipole_e_x0 for further details.
solver allows the user to choose from variations of the field solver. This has an impact on the actual dispersion relation that is solved. Valid options are:
- “yee” - Use the standard Yee solver.
- “custom” - Recommended option if not using Yee solver. Allows for using solvers that eliminate numerical Cherenkov radiation [2], remove unphysical fields surrounding relativistic charged particles and reduce numerical dispersion errors in
x1[3], remove dispersion errors and correct for time-stagger errors in the Lorentz force [4], or to use an explicitly defined set of coefficeints. See the emf_solver section for more information. - “stencil” - Use a linear combination of 3 methods for calculating the spatial derivatives, using different grid points, with relative weights defined by the k1 and k2 parameters defined below [5].
- “ndfx” - Use a Numerical Dispersion Free (along X1 direction) solver. IMPORTANT: Time step condition is changed to dt < dx1, not the usual Courant condition used for other solvers [6].
- “lehe” - Use the solver developed by R. Lehe. IMPORTANT: time step condition is changed to dt < dx1 [7].
Here’s an example of a el_mag_fld section that specifies an external magnetic field of 1.0 normalized units along x3.
el_mag_fld
{
ext_fld = "static",
type_ext_b(3) = "uniform", ! not really necessary since it is the default
b0(3) = 1.0d0,
}