17  Field Solver

17.5.6 Core command attributes

17.5.7 Fieldsolver type

FSTYPE selects the actual solver backend.

• FFT: standard open-boundary FFT-based particle-mesh solver
• FFTPERIODIC: FFT solver with periodic longitudinal treatment
• SAAMG: iterative irregular-domain solver
• P3M: mixed mesh plus short-range direct solver
• NONE: disable space-charge field solving

FFT solver is the most stable default path.

17.5.8 Domain Decomposition

PARFFTX, PARFFTY, and PARFFTT decide whether the corresponding mesh direction is distributed over MPI processes.

Legacy default:

• PARFFTX = FALSE
• PARFFTY = FALSE
• PARFFTT = TRUE

So the conventional decomposition is serial in x and y, parallel in z.

17.5.9 Number of Grid Points

MX, MY, and MT define the rectangular mesh resolution in x, y, and z. These values determine both the field resolution and the FFT problem size, so they are the main tuning parameters for accuracy and cost.

17.5.10 Boundary Conditions

Boundary conditions are specified independently per axis:

• BCFFTX: OPEN
• BCFFTY: OPEN
• BCFFTZ: OPEN or PERIODIC

Using PERIODIC in z is the standard way to model a DC beam rather than an isolated bunch.

17.5.13 Geometry

GEOMETRY attaches a list of geometry objects that define the boundary of the computational domain for the irregular-domain solver. This option is relevant to SAAMG workflows.

17.5.14 Iterative Solver

ITSOLVER selects the Krylov or direct linear solver used by the iterative field-solver family.

For SAAMG, the documented choices are:

• CG (default)
• BICGSTAB
• GMRES

17.5.15 Interpolation for Boundary Points

INTERPL controls how grid points near the irregular boundary are interpolated.

Allowed values:

• CONSTANT
• LINEAR (default)
• QUADRATIC

This parameter is specific to SAAMG.

17.5.16 Tolerance

TOL is the convergence tolerance for the iterative solver.

Default:

• TOL = 1e-8

17.5.17 Maximal Iterations

MAXITERS limits the number of iterations taken by the iterative solver.

Default:

• MAXITERS = 100

17.5.18 Preconditioner Behavior

PRECMODE controls how aggressively the SAAMG preconditioner is rebuilt or reused.

This parameter should only be changed deliberately, because it affects both performance and solver robustness.

17.5.19 Cut-off Radius

RC is the short-range cutoff radius for the P3M solver in the boosted frame. Particles separated by less than this radius are included in the direct particle-particle correction.

Default:

• RC = 0

This corresponds to disabling the direct short-range correction.

17.5.20 Interaction splitting parameter

ALPHA controls the balance between the short-range and mesh parts of the P3M Green-function split. Large ALPHA gives greater weight to the mesh part; small ALPHA gives greater weight to the particle-particle part.

It is commonly chosen as

\[ \alpha = C / r_c \tag{17.3}\]

with C of order one and r_c the cutoff radius.

Default:

• ALPHA = 1e8

This parameter is only used for GREENSF=STANDARD.

17.5.21 Number of Energy Bins

ENBINS selects how many energy bins are used when the bunch is split for multi-frame space-charge treatment. In cyclotron multi-bunch mode this should not be smaller than NNEIGHBB.

MINSTEPFORREBIN defines after how many steps the temporarily split energy-bin representation is merged back into one.

17.6 Adaptive Mesh Refinement (AMR) Solver

The AMR path extends the FIELDSOLVER command with hierarchy and refinement controls. It is enabled by compiling OPAL with ENABLE_AMR=ON and enabling OPTION, AMR=TRUE.

The legacy interface describes three AMR solver types:

• FMG
• ML
• AMR_MG

The hierarchy is defined from the base grid by the number of AMR levels, refinement ratios, blocking factors, and maximum grid sizes.

OPTION, AMR              = TRUE;
OPTION, AMR_REGRID_FREQ  = 10;
OPTION, AMR_YT_DUMP_FREQ = 100000;

REAL Edes      = .072;
REAL turns     = 8;
REAL nstep     = 360;
REAL frequency = 50.650;

ring: CYCLOTRON, ...;
rf0: RFCAVITY, ...;
rf1: RFCAVITY, ...;
rf2: RFCAVITY, ...;
rf3: RFCAVITY, ...;
rf4: RFCAVITY, ...;
l1: LINE = (ring, rf0, rf1, rf2, rf3, rf4);

Dist1: DISTRIBUTION, ...;

Fs1: FIELDSOLVER, FSTYPE=AMR_MG,
                  MX=128, MY=128, MT=128,
                  PARFFTX=TRUE, PARFFTY=TRUE, PARFFTT=TRUE,
                  BCFFTX=OPEN, BCFFTY=OPEN, BCFFTZ=OPEN,
                  BBOXINCR=20, AMR_MAXLEVEL=2,
                  AMR_MAXGRIDX=32, AMR_MAXGRIDY=32, AMR_MAXGRIDZ=32,
                  AMR_BFX=16, AMR_BFY=16, AMR_BFZ=16,
                  AMR_REFX=2, AMR_REFY=2, AMR_REFZ=2,
                  AMR_DOMAIN_RATIO={1.0, 0.75, 0.75},
                  AMR_TAGGING="CHARGE_DENSITY", AMR_DENSITY=1.0e-9,
                  AMR_MG_VERBOSE=TRUE, AMR_MG_REBALANCE=TRUE, AMR_MG_REUSE=FULL,
                  ITSOLVER=SA, AMR_MG_NORM=LINF_NORM, AMR_MG_NSWEEPS=12;

beam1: BEAM, PARTICLE=PROTON, PC=P0, NPART=1e5, BCURRENT=2.0E-3, CHARGE=1.0, BFREQ=frequency;

SELECT, LINE=l1;

TRACK, LINE=l1, BEAM=beam1, MAXSTEPS=nstep*turns, STEPSPERTURN=nstep;
RUN, METHOD="CYCLOTRON-T", BEAM=beam1, FIELDSOLVER=Fs1, DISTRIBUTION=Dist1,
    MBMODE=FORCE, TURNS=11, MB_BINNING=GAMMA_BINNING, MB_ETA=0.25;

ENDTRACK;
STOP;