MomentumGrid¶
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class
MomentumGrid¶
Class for the grid in momentum space.
Properties¶
Resolution parameters:¶
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Nxi¶
number of Legendre modes used to represent the pitch-angle coordinate (determines resolution in xi=cos(theta))
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Ny¶
number of points in the grid used to represent momentum
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yMax¶
maximum of the momentum grid, in units of y=gamma*v/v_{th}. Together, Ny and yMax determine the resolution in momentum
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y¶
momentum grid p/p_thermal, where p_thermal is treated classically
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y2¶
y.^2
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y4¶
y.^4
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x¶
v/v_thermal x2. x.^2
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gamma¶
Relativistic gamma function
Differential Calculation Params:¶
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ddy¶
Differential operator, differenting with respect to y, requiers vector of length same as y
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d2dy2¶
Same as ddy but second derivetive
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yWeights¶
Integration operator with respect to y, same limitation as ddy (row vector)
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ddx¶
Differential operator with respect to x d2dx2 - second order differential operator with respect to x
Numerical grid parameters:¶
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yGridMode¶
Specifies how the points on the momentum grid are chosen
- uniform grid on [0, dy*(Ny-1)]
- nonuniform grid, remapped using y = scaleFactor*tan(pi*a*s/2)
- nonuniform grid, remapped using y = -scaleFactor*ln(a-s)
- nonuniform grid, remapped using y = scaleFactor*s/(a-s)
4. nonuniform grid, remapped using y = s^2 + gridParameter*s, where gridParameter>0 (default)
- nonuniform grid, smooth tanh step between dense bulk and
sparse tail. gridParameter controls the spacing in the bulk (and is in units of y). gridStepWidth controls the width of the smooth step between bulk and tail, and gridStepPosition its position (in units of y_c). gridParameter=1/15, gridStepWidth=1/50 and gridStepPosition=2 is a good starting point, not implemented yet Above, s is a uniform grid and a is a constant close to 1. When running a CODE+GO calculation, yGridMode must be either 0 or 4. The reason is that only these two remappings are able to handle varying grids in the required way.
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gridParameter¶
for use with yGridMode 4 and 5
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gridStepWidth¶
for use with yGridMode 5
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gridStepPosition¶
for use with yGridMode 5
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yMaxBoundaryCondition¶
Boundary condition at yMax (does this more belong in the equation settings?)
- Dirichlet: F=0 (default)
- Robin: dF/dy + (2/y)*F=0, which forces F to behave like 1/y^2
- Do not apply a boundary condition at yMax
- Dirichlet: F=0, with a bit of extra d2dy2 added at the last few grid points to eliminate ringing
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artificialDissipationStrength¶
only used with yMaxBoundaryCondition=4 to control the amount of ringing
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artificialDissipationWidth¶
in momentum (how close to yMax). Only used with yMaxBoundaryCondition=4 to control the amount of ringing
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VERSION¶
Functions¶
Set functions¶
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setResolution(this, varargin)¶
Sets resolution parameters, standard matlab syntax (‘name’,value). Also reinitializes the momentum grid
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setNxi(this, Nxi)¶
Sets Nxi to passed value and also reinitializes the momentum grid
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setNy(this, Ny)¶
Sets Ny to passed value and also reinitializes the momentum grid
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setyMax(this, yMax)¶
Sets yMax to passed value and also reinitializes the momentum grid
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setyGridMode(this, yGridMode)¶
Sets yGridMode to passed value and also reinitializes the momentum grid
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setgridParameter(this, gridParameter)¶
Sets gridParameter to passed value and also reinitializes the momentum grid
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setgridStepWidth(this, gridStepWidth)¶
Sets gridStepWidth to passed value and also reinitializes the momentum grid
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setgridStepPosition(this, gridStepPosition)¶
Sets gridStepPosition to passed value and also reinitializes the momentum grid
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setyMaxBoundaryCondition(this, yMaxBoundaryCondition)¶
Sets yMaxBoundaryCondition to passed value and also reinitializes the momentum grid
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setartificialDissipationStrength(this, artificialDissipationStrength)¶
Sets artificialDissipationStrength to passed value and also reinitializes the momentum grid
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setartificialDissipationWidth(this, artificialDissipationWidth)¶
Sets artificialDissipationWidth to passed value and also reinitializes the momentum grid