Profile

This section configures the density profile for the particle species and is generally required in the input file. If parameters are not specified, the code will default to a uniform density profile with density = 1.0. One of these sections should exist for every species we intend to use.

There are various types of profiles allowed, which are specified in the species portion of the input deck. The currently available types are “standard”/”profile”, “constq”, “beamfocus” and “file”, each of which are described below.

Standard profile

This profile type is selected by setting init_type to “standard” or “profile” in the species portion of the input deck. It accepts the following data:

density, real, default, = 1.0
den_min, real, default = 0.0
profile_type(x_dim), character(*), default = “uniform” (if num_x > 0 then defaults to “piecewise-linear”)

num_x, integer, default = -1
x(num_x, x_dim), real, default = -Inf
fx(num_x, x_dim), real, default = 0.0

gauss_center(x_dim), real, default = 0.0
gauss_sigma(x_dim), real, default = Inf
gauss_range(2,x_dim), real, default = {-Inf, Inf}
gauss_n_sigma(x_dim), integer, default = 0

channel_dir, integer, default = 1
channel_r0, float, default = 0.0
channel_depth, float, default = 0.0
channel_size, float, default = 0.0
channel_center(x_dim-1), float, default = 0.0
channel_wall, float, default = 0.0
channel_pos(2), float, default = 0.0
channel_bottom, float, default = 1.0

sphere_center(x_dim), float, default = 0.0
sphere_radius, float, default = 0.0

math_func_expr, character(*), default = “NO_FUNCTION_SUPPLIED!”

density - specifies a global multiplication factor for the density profile. Regardless of which profile type you choose, the final density value will be density * profile value (see below). This parameter can be used to set the density for the sphere and uniform density profile types as these default to 1.0 in the appropriate regions.

den_min - specifies the minimum density for injecting particles. Particles are only injected when the specified density is above this threshold. This parameter is ignored if used in a species connected to a neutral or neutral_mov_ions particle source.

profile_type - specifies the profile type to use. There are two groups of density profiles that can be selected: (1) functions that are separable into functions that depend only on one of the coordinates, i.e., $f(x_1,x_2) = f_1(x_1) \times f_2(x_2)$ and (2) arbitrary functions. If you choose the use the first group, you can use piecewise-linear and Gaussian functions for any of the $f_i(x_i)$. If you choose the second group, you can use one of the following function types: uniform, channel, sphere or a specified mathematical function. You cannot mix functions from the two groups.

If using separable functions, each component of the profile_type parameter must be set to one of the following values:

“piecewise-linear” - uses a piecewise-linear function defined by the num_x, x and fx parameters. See these parameters for details.
“gaussian” - uses a Gaussian function defined by the x_cent, f_cent, x_sigm, and x_range parameters. See these parameters for details.

Here’s an example for a 3D run using piecewise-linear functions in the x1 and x2 direction and a Gaussian function in the x3 direction:

  profile_type(1:3) = "piecewise-linear", "piecewise-linear", "gaussian",

If using an arbitrary function, you should set the first or all the components of profile type to one of the following values:

“uniform” - use a uniform density profile. The density value is set using the density parameter.
“channel” - use a parabolic channel density profile. Channel parameters are set using the channel_dir, channel_r0, channel_depth, channel_size, channel_center, channel_wall, channel_pos and channel_bottom. See these parameters for details.
“sphere” - use a spheric density profile. The density value is set using the density parameter. Sphere parameters are set using the sphere_center and sphere_radius parameters. See these parameters for details.
“math func” - use the mathematical function supplied in the math_func_expr parameter to define the density profile. See this parameter for details.

Here’s an example using a spheric density profile:

  profile_type = "sphere",

num_x, x, fx - specify the parameters for the piecewise-linear function we intend to use. The num_x parameter represents the number of points to use in the piecewise-linear function (note that by setting this parameter to a value > 0 you also default your profile type to piecewise-linear). The x(k,i) and fx(k,i) parameters represent the position and density of the i-th direction for the k-th position. If profile_type(i) is not equal to “piecewise-linear”, the values specified are silently ignored. The index k ranges from 1 to num_x, and this range is the same for every i (ranging from 1 to x_dim). Here’s an example for a 6-point piecewise-linear function in the x2 direction:

  x(1:6,2) = 0., 2.0, 2.1, 4.9, 5.0, 1000.,
  fx(1:6,2) = 0., 0., 1., 1., 0., 0.,

gauss_center, gauss_sigma, gauss_range, gauss_n_sigma - specify the parameters for the Gaussian function we intend to use. The gauss_center(i), gauss_sigma(i) and gauss_range(\*,i) parameters represent the center, sigma and range for the Gaussian on the i-th direction, respectively. If profile_type(i) is not equal to “gaussian” the values specified are silently ignored. The gauss_range(k,i) represent the lower (k=1) and upper (k=2) limits for which the Gaussian function is evaluated. Outside these limits a value of 0 is returned. The gauss_n_sigma(i) parameter, if specified, takes precedence over the gauss_range(i) parameter and sets the range to include gauss_n_sigma(i) number of sigmas on either side of the center. Here’s an example for a Gaussian function in the x1 direction with sigma = 1.4142, centered about x1 = 10.0, with a peak value of 2.0, defined for $5.0 < x_1 < 15.0$:

  gauss_center(1) = 10.0,
  gauss_sigma(1) = 1.4142,
  gauss_range(1:2,1) = 5.0, 15.0,
  density = 2.0,

channel_dir, channel_r0, channel_depth, channel_size, channel_center, channel_wall, channel_pos, channel_bottom - specify the parameters for a parabolic channel. The channel_dir parameter specifies channel symmetry axis. If profile_type(1) is not set to “channel”, the values specified are silently ignored. The density of the channel will be channel_bottom + channel_depth * (||x_perp - channel_center||/channel_r0)^2 for ||x_perp - channel_center|| < channel_size/2, where x_perp is the position perpendicular to the symmetry axis. For ||x_perp - channel_center|| >= channel_size/2, the density will either be constant (channel_wall <= 0.0) or fall off linearly to 0.0 along a distance of channel_wall. The channel_pos(k) parameter specifies the beggining (k=1) and end (k=2) of the channel along the symmetry axis. The channel_center parameter represents the coordinates perpendicular to the symmetry axis, i.e., in 3D, if channel_dir = 2, then channel_center = { center x1, center x3 }. Here’s an example for a 2D run.

  channel_dir = 1,
  channel_r0 = 0.349308,
  channel_depth = 32.727,
  channel_size = 2.09585,
  channel_center = 1.74654,
  channel_wall = 0.174654,
  channel_pos(1:2) = 15.0659, 10000.0,
  channel_bottom = 1.0,

sphere_center, sphere_radius - specify the parameters for a spheric density profile. If profile_type(1) is not set to “sphere”, the values specified are silently ignored. The density value will be 1.0 for || x - sphere_center || <= sphere_radius and zero otherwise. The density parameter should be used to change the density value inside the sphere.

math_func_expr - specifies the mathematical function to be used to define the profile. If profile_type(1) is not set to “math func”, this value is silently ignored. 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. Here’s an example defining a pac-man-shaped density in 2D:

  math_func_expr = "if((x1-6.4)^2+(x2-6.4)^2<6.4^2,
                       if( (abs(x2-6.4) < 4.5-x1),0.,1.),
                       0.0)",

Constant charge

This profile type is selected by setting init_type to “constq” in the species portion of the input deck. This profile should be used when particles are desired to have equal charge (rather than a fixed number of particles per cell). This profile only works for separable density functions and is thus incompatible with the “channel” and “sphere” profile types. It accepts all of the same parameters as the standard profile, except for the following additional parameter:

sample_rate(x_dim), integer, default = 32

sample_rate - specify the number of sampling points per cell in each dimension.

Beam focus

This profile type is selected by setting init_type to “beamfocus” in the species portion of the input deck. This profile should be used when injecting a beam-like particle distribution with a specified Gaussian width, focus, etc. It accepts the following data:

density, real, default, = 1.0
den_min, real, default = 0.0

gauss_center(x_dim), real, default = 0.0
gauss_sigma(x_dim), real, default = Inf
gauss_range(2,x_dim), real, default = {-Inf, Inf}
gauss_n_sigma(x_dim), integer, default = 0

focal_dist(3), real, default = 0.0
alpha(3), real, default = 0.0
uth(3), real, default = 0.0
gamma, real, default = 1.0

density - specifies a global multiplication factor for the density profile. Regardless of which profile type you choose the final density value will be density * profile value (see below). This parameter can used to set the density for the sphere and uniform density profile types as these default to 1.0 in the appropriate regions.

den_min - specifies the minimum density for injecting particles. Particles are only injected when the specified density (see profile section) is above this threshold. This parameter is ignored if used in a species connected to a neutral or neutral_mov_ions particle source.

focal_dist - specify the focal plane distance after acceleration for each dimension.

alpha - specify the amount to rotate in the momentum-position phasespace along each dimension/component. The momentum is transformed according to p(i) = p(i) - x(i) * alpha(i) for the i-th dimension.

uth - specify the beam thermal momentum at the focal plane in each dimension.

gamma - specifies the Lorentz factor, $\gamma$, associated with the longitudinal momentum (p1) of the particles after acceleration.

Initialization from a RAW particle file

This profile type is selected by setting init_type to “file” in the species portion of the input deck. This profile initializes a particle distribution as specified by a RAW particle file. It accepts the following data:

file_name, character(*), default = “”
x1_offset, real, default = 0.0
q_mult, real, default = 1.0

file_name - specify the path to the file that contains the RAW particle data to be read in.

x1_offset - specify a position offset in the x1-direction for all particles. When specified, the position of a given particle will be set as x1_part = x1_raw - x1_offset.

q_mult - specify a charge scaling factor that multiplies the RAW particle charge at initialization.