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Beam Dynamic Calculation by NVIDIA® CUDA Technology

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7 July 2009

Beam Dynamic Calculation by NVIDIA® CUDA Technology

E. Perepelkin, V. Smirnov, and S. Vorozhtsov

JINR, Dubna

- Cyclotron beam dynamic problems [1]:
- Losses on geometry
- Space Charge effects
- Optimization of the central region [2]

- CBDA [3] code calculations:
- OpenMP ( by CPU )
- CUDA ( by GPU )
__________________________________________________________________

[1] Beam injection and extraction of RIKEN AVF cyclotron, A. Goto, CNS-RIKEN Workshop on Upgrade of AVF Cyclotron, CNS Wako Campus, 3-4 March 2008

[2] SPIRAL INFLECTORS AND ELECTRODES IN THE CENTRAL REGION OF THE VINCY CYCLOTRON, E. Perepelkin, A. Vorozhtsov, S. Vorozhtsov, P. Beličev, V. Jocić, N. Nešković, etc., Cyclotrons and Their Applications 2007, Eighteenth International Conference

[3] CBDA - CYCLOTRON BEAM DYNAMICS ANALYSIS CODE, E. Perepelkin, S. Vorozhtsov, RuPAC 2008, Zvenigorod, Russia

Injection line

Dee

ESD

Magnet sectors

Inflector

Electric field

G1

Magnetic field

Axial channel

Magnetic field

φRF = 15°

φRF = 13°

φRF = 10°

φRF = 28°

S0

S1

S2

S3

S4

- About 5 different variants – minimum
- Many ion species – accelerated
- Very complicated structure
- Multi macro particle simulations for SC dominated beams

One run requires ~ several days of computer time

Open Multi-Processing

( Open MP )

Beam phase space projectionsat the inflector entrance

Blue points – PIC by FFT (Grid: 25 x 25 x 25 )Red points – PP

10,000 particlesNo geometry losses

Compute Unified Device Architecture

( CUDA )

128 SP ( Streaming Processors )

- __global__ void Track ( field maps, particles coordinates )
- Calculate particle motion in electromagnetic field maps

- __global__ void Losses ( geometry, particles coordinates )
- Calculate particle losses on the structure

- __global__ void Rho ( particles coordinates )
- Produce charge density for SC effects

- __global__ FFT ( charge density )
- FFT method ( analysis / synthesis )

- __global__ PoissonSolver ( Fourie’s coefficients )
- Find solution of Poisson equation

- __global__ E_SC ( electric potential )
- Calculate electric field by E = -grad( U )

- Function with many parameters. Use variable type __constant__:
- __device__ __constant__ float d_float[200];
- __device__ __constant__ int d_int[80];

- Particle number corresponds
- int n = threadIdx.x+blockIdx.x*blockDim.x;

- Number of “if, goto, for” should be decreased;

- Geometry structure consists from triangles. Triangles coordinates stored in __shared__ variables. This feature gave drastically increase performance
- int tid = threadIdx.x; - used for parallel copying data to shared memory

- Particle number corresponds to
- int n = threadIdx.x+blockIdx.x*blockDim.x;
- Check particles and triangle match

- Calculate charge impact in the nodes of mesh from particle with number
int n = threadIdx.x+blockIdx.x*blockDim.x;

Cell 7

Cell 8

Node

Cell 6

Cell 5

Cell 3

Cell 2

Cell 1

- Used real FFT for sin(πn/N) basis functions;
- 3D transform consist from three 1D FFT for each axis: X, Y, Z
- int n = threadIdx.x+blockIdx.x*blockDim.x;
k=(int)(n/(NY+1));

j=n-k*(NY+1);

m=j*(NX+1)+k*(NX+1)*(NY+1);

FFT_X[i+1]=Rho[i+m];

n = j + k*(NY+1)

NY

NZ

- int n = threadIdx.x+blockIdx.x*blockDim.x;
- Uind(i,j,k) = Uind(i,j,k) / ( kxi2 + kyj2 + kzk2 )
ind(i,j,k)=i+j*(NX+1)+k*(NX+1)*(NY+1);

k=(int)(n/(NX+1)*(NY+1));

j=(int)(n-k*(NX+1)*(NY+1))/(NX+1);

i=n-j*(NX+1)-k*(NX+1)*(NY+1);

- int n = threadIdx.x+blockIdx.x*blockDim.x+st_ind

Un + ( NX + 1 )( NY + 1 )

Un + ( NX + 1 )

Un

Un - 1

Un - ( NX + 1 )

Un + 1

Un - ( NX + 1 )( NY + 1 )

* Mesh size: 25 x 25 x 25. Particles: 100,000. Triangles: 2054

no SC

Losses 24%

SC

Losses 94%

I = 4 mA

- Very chipper technology
- Increasing of performance at power 1.5 gave chance to produce the complex cyclotron modeling
- Careful programming
- Expand this method for calculation of beam halo and etc.