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### fix field/grid command

Syntax:

```fix ID field/grid axvar ayvar azvar
```

ID is documented in fix command field/grid = style name of this fix command axvar,ayvar,azvar = names of grid-style variables for acceleration components:ul

Examples:

```fix 1 field/grid gradBx gradBy NULL
```

Description:

Specify the formulas used to calculate the acceleration effect of an external field on particle motion. The ID of this fix can be used by the global field grid command which applies the field when particles are advected during a simulation run. This is done by invoking a method in this fix, which evaluates the specified grid-style variables.

Each of the axvar, ayvar, and azvar arguments is the name of a grid-style variable. The variables should compute the x,y,z components of acceleration applied at the center point of each grid cell in the simulation. Any of the three variables can be specified as NULL, which means there is no acceleration in that dimension.

Each timestep when a particle is advected the acceleration vector (a) for the grid cell it is in acts as a perturbation on straight-line motion which affects both the end-of-timestep position (x) and velocity (v) vectors of the particle:

```xnew = x + dt*v + 0.5*a*dt^2
vnew = v + dt*a
```

Note that the formulas encoded by the axvar, ayvar, and azvar variables should produce values that are in units of acceleration (distance/time^2, see the units command), not force. And they should not include the timestep (dt) value in the formulas above. That is applied by SPARTA during advection.

See the variable doc page for a description of the formula syntax allowed for grid-style variables. They can include references to the grid vectors xc, yc, and zc for the grid cell center point. Using these values in a formula can enable a spatially-dependent field. The formulas can also include the current timestep and timestep size (dt) to enable a time-dependent field.

NOTE still need to figure this out: And they can include properties of the particle, such as its mass or magnetic moment.

Note that the global field command provides three alternatives for specifying an external field:

```global field constant ...     # field is constant in space and time
global field particle ...     # field is applied on a per particle basis
global field grid ...         # field is applied on a per grid cell basis
```

This fix is only used for per-grid fields. It should only be used for fields which vary spatially or in time; otherwise use the constant option which will be much more efficient. The use of per-grid variables allows the field to vary spatially as a function of the grid cell center point. It also allows the field to vary in time by having the variables use the current timestep.

NOTE still need to figure out how to do this: The field can also depend on particle attributes, such as its mass and magnetic moment (for a B field).

Note that use of the global field grid command with this fix will evaluate the specified grid-style variables as often as requested. For a field that has no time-ependence, you can specificy it only be evaluated once at the beginning of a run. For a field that is time-dependent you can choose how often to recompute the field, depending on how fast it varies.

The fix field/particle command is an alternative which will typically run much slower, but be more accurate. When used with the global field particle command, the particle-style variables it uses are invoked every timestep using current particle positions. And the field calculation is done for each grid particle, not for each grid cell. The trade-off is that the fields it calculates for each particle is more accurate, but the simulation will typically run several times slower than it would with this fix.

Restart, output info: