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7 July 2009. Beam Dynamic Calculation by NVIDIA® CUDA Technology. E. Perepelkin, V. Smirnov, and S. Vorozhtsov JINR, Dubna. Introduction. Cyclotron beam dynamic problems [1]: Losses on geometry Space Charge effects Optimization of the central region [2] CBDA [3] code calculations:

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Beam dynamic calculation by nvidia cuda technology

7 July 2009

Beam Dynamic Calculation by NVIDIA® CUDA Technology

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

JINR, Dubna


Introduction
Introduction

  • 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


Computer model of the cyclotron

Injection line

Dee

ESD

Magnet sectors

Computer model of the cyclotron


Regions of the field maps

Inflector

Electric field

G1

Magnetic field

Axial channel

Magnetic field

Regions of the field maps




Central region optimization

φRF = 15°

φRF = 13°

φRF = 10°

φRF = 28°

Central region optimization




Optimization process

S0

S1

S2

S3

S4

Optimization process



Very time consuming problem
Very time consuming problem

  • 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




Beam phase space projectionsat the inflector entrance


Beam phase space projections at the inflector exit
Beam phase space projectionsat the inflector exit

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


Calculation time
Calculation time

10,000 particlesNo geometry losses




Gpu structure
GPU structure

128 SP ( Streaming Processors )


Kernel functions
Kernel functions

  • __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


Kernel functions1
Kernel functions

  • __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 )


Global void track
__global__ void Track ( )

  • 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;


Global void losses
__global__ void Losses ( )

  • 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


Global void rho
__global__ void Rho

  • 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


Global fft
__global__ FFT ( )

  • 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


Global poissonsolver
__global__ PoissonSolver ( )

  • 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);


Global e sc
__global__ E_SC ( )

  • 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 )


Performance
Performance

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



Sc effect
SC effect

no SC

Losses 24%

SC

Losses 94%

I = 4 mA


Conclusions
Conclusions

  • 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.


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