A Glimpse of The Current Space Charge EffectsCalculation Routines

He Zhang

Department of Physics and AstronomyMichigan State University

Group talk, Sep. 28th, 2009, MSU

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

Two Categories

From 1960s till now, many space charge routines have beendeveloped. They can be classified in two categories.[1]

The first, Particle to Particle Interaction (PPI) procedure.

Track macroparticles.Find an expression of the particle density distribution.Calculate the field be integrating the expression.

The second, Particle In Cell (PIC) codes.

Reassign the charges on a mesh.Solve Poisson equation to get the field on the nodes of themesh.Calculate the field on each particle by interpolation.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

Two Categories

From 1960s till now, many space charge routines have beendeveloped. They can be classified in two categories.[1]

The first, Particle to Particle Interaction (PPI) procedure.

Track macroparticles.Find an expression of the particle density distribution.Calculate the field be integrating the expression.

The second, Particle In Cell (PIC) codes.

Reassign the charges on a mesh.Solve Poisson equation to get the field on the nodes of themesh.Calculate the field on each particle by interpolation.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

Two Categories

From 1960s till now, many space charge routines have beendeveloped. They can be classified in two categories.[1]

The first, Particle to Particle Interaction (PPI) procedure.

Track macroparticles.Find an expression of the particle density distribution.Calculate the field be integrating the expression.

The second, Particle In Cell (PIC) codes.

Reassign the charges on a mesh.Solve Poisson equation to get the field on the nodes of themesh.Calculate the field on each particle by interpolation.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

Two Categories

From 1960s till now, many space charge routines have beendeveloped. They can be classified in two categories.[1]

The first, Particle to Particle Interaction (PPI) procedure.

Track macroparticles.Find an expression of the particle density distribution.Calculate the field be integrating the expression.

The second, Particle In Cell (PIC) codes.

Reassign the charges on a mesh.Solve Poisson equation to get the field on the nodes of themesh.Calculate the field on each particle by interpolation.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

Two Categories

From 1960s till now, many space charge routines have beendeveloped. They can be classified in two categories.[1]

The first, Particle to Particle Interaction (PPI) procedure.

Track macroparticles.Find an expression of the particle density distribution.Calculate the field be integrating the expression.

The second, Particle In Cell (PIC) codes.

Reassign the charges on a mesh.Solve Poisson equation to get the field on the nodes of themesh.Calculate the field on each particle by interpolation.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

Two Categories

From 1960s till now, many space charge routines have beendeveloped. They can be classified in two categories.[1]

The first, Particle to Particle Interaction (PPI) procedure.

Track macroparticles.Find an expression of the particle density distribution.Calculate the field be integrating the expression.

The second, Particle In Cell (PIC) codes.

Reassign the charges on a mesh.Solve Poisson equation to get the field on the nodes of themesh.Calculate the field on each particle by interpolation.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

Two Categories

From 1960s till now, many space charge routines have beendeveloped. They can be classified in two categories.[1]

The first, Particle to Particle Interaction (PPI) procedure.

Track macroparticles.Find an expression of the particle density distribution.Calculate the field be integrating the expression.

The second, Particle In Cell (PIC) codes.

Reassign the charges on a mesh.Solve Poisson equation to get the field on the nodes of themesh.Calculate the field on each particle by interpolation.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

Two Categories

From 1960s till now, many space charge routines have beendeveloped. They can be classified in two categories.[1]

The first, Particle to Particle Interaction (PPI) procedure.

Track macroparticles.Find an expression of the particle density distribution.Calculate the field be integrating the expression.

The second, Particle In Cell (PIC) codes.

Reassign the charges on a mesh.Solve Poisson equation to get the field on the nodes of themesh.Calculate the field on each particle by interpolation.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-MAPRO2

MAPRO2 (1971) [2]

Use one macropartile to represent 105 to 107 real particles.

Assume the whole bunch has a Gaussian distribution ofmacroparticles.

χ(x , y , z) = χ0 exp{−1

2(x2

a2+

y2

b2+

z2

c2)}, χ0 =

4

(2π)3/2

N

abc,

where 4N is the total amount of macroparticles.

The field on each macroparticle can be calculated bynumerical integration.

Limits: Ellipsoidal symmetry, Gaussian distribution.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-MAPRO2

MAPRO2 (1971) [2]

Use one macropartile to represent 105 to 107 real particles.

Assume the whole bunch has a Gaussian distribution ofmacroparticles.

χ(x , y , z) = χ0 exp{−1

2(x2

a2+

y2

b2+

z2

c2)}, χ0 =

4

(2π)3/2

N

abc,

where 4N is the total amount of macroparticles.

The field on each macroparticle can be calculated bynumerical integration.

Limits: Ellipsoidal symmetry, Gaussian distribution.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-MAPRO2

MAPRO2 (1971) [2]

Use one macropartile to represent 105 to 107 real particles.

Assume the whole bunch has a Gaussian distribution ofmacroparticles.

χ(x , y , z) = χ0 exp{−1

2(x2

a2+

y2

b2+

z2

c2)}, χ0 =

4

(2π)3/2

N

abc,

where 4N is the total amount of macroparticles.

The field on each macroparticle can be calculated bynumerical integration.

Limits: Ellipsoidal symmetry, Gaussian distribution.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-MAPRO2

MAPRO2 (1971) [2]

Use one macropartile to represent 105 to 107 real particles.

Assume the whole bunch has a Gaussian distribution ofmacroparticles.

χ(x , y , z) = χ0 exp{−1

2(x2

a2+

y2

b2+

z2

c2)}, χ0 =

4

(2π)3/2

N

abc,

where 4N is the total amount of macroparticles.

The field on each macroparticle can be calculated bynumerical integration.

Limits: Ellipsoidal symmetry, Gaussian distribution.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-MAPRO2

MAPRO2 (1971) [2]

Use one macropartile to represent 105 to 107 real particles.

Assume the whole bunch has a Gaussian distribution ofmacroparticles.

χ(x , y , z) = χ0 exp{−1

2(x2

a2+

y2

b2+

z2

c2)}, χ0 =

4

(2π)3/2

N

abc,

where 4N is the total amount of macroparticles.

The field on each macroparticle can be calculated bynumerical integration.

Limits: Ellipsoidal symmetry, Gaussian distribution.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-SC3DELP

SC3DELP (1991)[3]

Assume the bunch has an ellipsoidal symmetry, the field isEx = q abc x

2ε0

∫∞

0n(t)ds

(a2+s)3/2(b2+s)1/2(c2+s)1/2 ,

t = t(x , y , z , s) = x2/(a2 + s) + y2/(b2 + s) + z2/(c2 + s),and analogous expressions are valid for Ey and Ez .

Use Fourier description, get the particle-density function n(t)from a distribution of macroparticles at a given time.

The the field can be calculated by numerical distribution.

Limits: Ellipsoidal symmetry.

Code TOPKARK, use this routine, generate the map withspace charge effects by DA method. [5]

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-SC3DELP

SC3DELP (1991)[3]

Assume the bunch has an ellipsoidal symmetry, the field isEx = q abc x

2ε0

∫∞

0n(t)ds

(a2+s)3/2(b2+s)1/2(c2+s)1/2 ,

t = t(x , y , z , s) = x2/(a2 + s) + y2/(b2 + s) + z2/(c2 + s),and analogous expressions are valid for Ey and Ez .

Use Fourier description, get the particle-density function n(t)from a distribution of macroparticles at a given time.

The the field can be calculated by numerical distribution.

Limits: Ellipsoidal symmetry.

Code TOPKARK, use this routine, generate the map withspace charge effects by DA method. [5]

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-SC3DELP

SC3DELP (1991)[3]

Assume the bunch has an ellipsoidal symmetry, the field isEx = q abc x

2ε0

∫∞

0n(t)ds

(a2+s)3/2(b2+s)1/2(c2+s)1/2 ,

t = t(x , y , z , s) = x2/(a2 + s) + y2/(b2 + s) + z2/(c2 + s),and analogous expressions are valid for Ey and Ez .

Use Fourier description, get the particle-density function n(t)from a distribution of macroparticles at a given time.

The the field can be calculated by numerical distribution.

Limits: Ellipsoidal symmetry.

Code TOPKARK, use this routine, generate the map withspace charge effects by DA method. [5]

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-SC3DELP

SC3DELP (1991)[3]

Assume the bunch has an ellipsoidal symmetry, the field isEx = q abc x

2ε0

∫∞

0n(t)ds

(a2+s)3/2(b2+s)1/2(c2+s)1/2 ,

t = t(x , y , z , s) = x2/(a2 + s) + y2/(b2 + s) + z2/(c2 + s),and analogous expressions are valid for Ey and Ez .

Use Fourier description, get the particle-density function n(t)from a distribution of macroparticles at a given time.

The the field can be calculated by numerical distribution.

Limits: Ellipsoidal symmetry.

Code TOPKARK, use this routine, generate the map withspace charge effects by DA method. [5]

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-SC3DELP

SC3DELP (1991)[3]

Assume the bunch has an ellipsoidal symmetry, the field isEx = q abc x

2ε0

∫∞

0n(t)ds

(a2+s)3/2(b2+s)1/2(c2+s)1/2 ,

t = t(x , y , z , s) = x2/(a2 + s) + y2/(b2 + s) + z2/(c2 + s),and analogous expressions are valid for Ey and Ez .

Use Fourier description, get the particle-density function n(t)from a distribution of macroparticles at a given time.

The the field can be calculated by numerical distribution.

Limits: Ellipsoidal symmetry.

Code TOPKARK, use this routine, generate the map withspace charge effects by DA method. [5]

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-SC3DELP

SC3DELP (1991)[3]

Assume the bunch has an ellipsoidal symmetry, the field isEx = q abc x

2ε0

∫∞

0n(t)ds

(a2+s)3/2(b2+s)1/2(c2+s)1/2 ,

t = t(x , y , z , s) = x2/(a2 + s) + y2/(b2 + s) + z2/(c2 + s),and analogous expressions are valid for Ey and Ez .

Use Fourier description, get the particle-density function n(t)from a distribution of macroparticles at a given time.

The the field can be calculated by numerical distribution.

Limits: Ellipsoidal symmetry.

Code TOPKARK, use this routine, generate the map withspace charge effects by DA method. [5]

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-SCHERM

SCHERM (1996)[1]

Assume the bunch has an ellipsoidal symmetry in transversedirection, no limit in longitudinal direction.

Use two/three Gaussian function to fit the longitudinal shape.

The field of each bunch can be calculated byEx = q abc x

2ε0

∫∞

0n(t)ds

(a2+s)3/2(b2+s)1/2(c2+s)1/2 , with ana logous

expressions for Ey and Ez .

The particle-density distribution can be expressed by Hermiteexpansion of the macroparticle distribution at a given time.

Then the field can by numerically integrated.

Limits: Ellipsoidal symmetry in transverse direction.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-SCHERM

SCHERM (1996)[1]

Assume the bunch has an ellipsoidal symmetry in transversedirection, no limit in longitudinal direction.

Use two/three Gaussian function to fit the longitudinal shape.

The field of each bunch can be calculated byEx = q abc x

2ε0

∫∞

0n(t)ds

(a2+s)3/2(b2+s)1/2(c2+s)1/2 , with ana logous

expressions for Ey and Ez .

The particle-density distribution can be expressed by Hermiteexpansion of the macroparticle distribution at a given time.

Then the field can by numerically integrated.

Limits: Ellipsoidal symmetry in transverse direction.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-SCHERM

SCHERM (1996)[1]

Assume the bunch has an ellipsoidal symmetry in transversedirection, no limit in longitudinal direction.

Use two/three Gaussian function to fit the longitudinal shape.

The field of each bunch can be calculated byEx = q abc x

2ε0

∫∞

0n(t)ds

(a2+s)3/2(b2+s)1/2(c2+s)1/2 , with ana logous

expressions for Ey and Ez .

The particle-density distribution can be expressed by Hermiteexpansion of the macroparticle distribution at a given time.

Then the field can by numerically integrated.

Limits: Ellipsoidal symmetry in transverse direction.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-SCHERM

SCHERM (1996)[1]

Assume the bunch has an ellipsoidal symmetry in transversedirection, no limit in longitudinal direction.

Use two/three Gaussian function to fit the longitudinal shape.

The field of each bunch can be calculated byEx = q abc x

2ε0

∫∞

0n(t)ds

(a2+s)3/2(b2+s)1/2(c2+s)1/2 , with ana logous

expressions for Ey and Ez .

The particle-density distribution can be expressed by Hermiteexpansion of the macroparticle distribution at a given time.

Then the field can by numerically integrated.

Limits: Ellipsoidal symmetry in transverse direction.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-SCHERM

SCHERM (1996)[1]

Assume the bunch has an ellipsoidal symmetry in transversedirection, no limit in longitudinal direction.

Use two/three Gaussian function to fit the longitudinal shape.

The field of each bunch can be calculated byEx = q abc x

2ε0

∫∞

0n(t)ds

(a2+s)3/2(b2+s)1/2(c2+s)1/2 , with ana logous

expressions for Ey and Ez .

The particle-density distribution can be expressed by Hermiteexpansion of the macroparticle distribution at a given time.

Then the field can by numerically integrated.

Limits: Ellipsoidal symmetry in transverse direction.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-SCHERM

SCHERM (1996)[1]

Assume the bunch has an ellipsoidal symmetry in transversedirection, no limit in longitudinal direction.

Use two/three Gaussian function to fit the longitudinal shape.

The field of each bunch can be calculated byEx = q abc x

2ε0

∫∞

0n(t)ds

(a2+s)3/2(b2+s)1/2(c2+s)1/2 , with ana logous

expressions for Ey and Ez .

The particle-density distribution can be expressed by Hermiteexpansion of the macroparticle distribution at a given time.

Then the field can by numerically integrated.

Limits: Ellipsoidal symmetry in transverse direction.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-SCHERM

SCHERM (1996)[1]

Assume the bunch has an ellipsoidal symmetry in transversedirection, no limit in longitudinal direction.

Use two/three Gaussian function to fit the longitudinal shape.

The field of each bunch can be calculated byEx = q abc x

2ε0

∫∞

0n(t)ds

(a2+s)3/2(b2+s)1/2(c2+s)1/2 , with ana logous

expressions for Ey and Ez .

The particle-density distribution can be expressed by Hermiteexpansion of the macroparticle distribution at a given time.

Then the field can by numerically integrated.

Limits: Ellipsoidal symmetry in transverse direction.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-Improved SCHERM

Improved SCHERM (1996) [4]

The charge density distribution of a 3D bunch (without anysymmetry assumption) can be expressed as

ρ(xa, y

b, z

c) =

∑

i ,j ,k

AijkHi (xa)Hj(

yb)Hk( z

c) exp(− x2

2a2 −y2

2b2 −z2

2c2 )

with Aijk = q

(2π)3/2 i !j!k!

N∑

n=1Hi (

xn

a)Hj (

yn

b)Hk( zn

c).

So the charge density distribution can be considered as a

Gaussian, ρ0(x , y , z) = A000 exp(− x2

2a2 −y2

2b2 −z2

2c2 ), with somecorrections.

The field due to the Gaussian can be numerically integratedas mentioned before. The field due to the other items canalso be numerically calculated by some tricks.

No limits on the bunch shape and charge distribution.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-Improved SCHERM

Improved SCHERM (1996) [4]

The charge density distribution of a 3D bunch (without anysymmetry assumption) can be expressed as

ρ(xa, y

b, z

c) =

∑

i ,j ,k

AijkHi (xa)Hj(

yb)Hk( z

c) exp(− x2

2a2 −y2

2b2 −z2

2c2 )

with Aijk = q

(2π)3/2 i !j!k!

N∑

n=1Hi (

xn

a)Hj (

yn

b)Hk( zn

c).

So the charge density distribution can be considered as a

Gaussian, ρ0(x , y , z) = A000 exp(− x2

2a2 −y2

2b2 −z2

2c2 ), with somecorrections.

The field due to the Gaussian can be numerically integratedas mentioned before. The field due to the other items canalso be numerically calculated by some tricks.

No limits on the bunch shape and charge distribution.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-Improved SCHERM

Improved SCHERM (1996) [4]

The charge density distribution of a 3D bunch (without anysymmetry assumption) can be expressed as

ρ(xa, y

b, z

c) =

∑

i ,j ,k

AijkHi (xa)Hj(

yb)Hk( z

c) exp(− x2

2a2 −y2

2b2 −z2

2c2 )

with Aijk = q

(2π)3/2 i !j!k!

N∑

n=1Hi (

xn

a)Hj (

yn

b)Hk( zn

c).

So the charge density distribution can be considered as a

Gaussian, ρ0(x , y , z) = A000 exp(− x2

2a2 −y2

2b2 −z2

2c2 ), with somecorrections.

The field due to the Gaussian can be numerically integratedas mentioned before. The field due to the other items canalso be numerically calculated by some tricks.

No limits on the bunch shape and charge distribution.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-Improved SCHERM

Improved SCHERM (1996) [4]

The charge density distribution of a 3D bunch (without anysymmetry assumption) can be expressed as

ρ(xa, y

b, z

c) =

∑

i ,j ,k

AijkHi (xa)Hj(

yb)Hk( z

c) exp(− x2

2a2 −y2

2b2 −z2

2c2 )

with Aijk = q

(2π)3/2 i !j!k!

N∑

n=1Hi (

xn

a)Hj (

yn

b)Hk( zn

c).

So the charge density distribution can be considered as a

Gaussian, ρ0(x , y , z) = A000 exp(− x2

2a2 −y2

2b2 −z2

2c2 ), with somecorrections.

The field due to the Gaussian can be numerically integratedas mentioned before. The field due to the other items canalso be numerically calculated by some tricks.

No limits on the bunch shape and charge distribution.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PPI-Improved SCHERM

Improved SCHERM (1996) [4]

The charge density distribution of a 3D bunch (without anysymmetry assumption) can be expressed as

ρ(xa, y

b, z

c) =

∑

i ,j ,k

AijkHi (xa)Hj(

yb)Hk( z

c) exp(− x2

2a2 −y2

2b2 −z2

2c2 )

with Aijk = q

(2π)3/2 i !j!k!

N∑

n=1Hi (

xn

a)Hj (

yn

b)Hk( zn

c).

So the charge density distribution can be considered as a

Gaussian, ρ0(x , y , z) = A000 exp(− x2

2a2 −y2

2b2 −z2

2c2 ), with somecorrections.

The field due to the Gaussian can be numerically integratedas mentioned before. The field due to the other items canalso be numerically calculated by some tricks.

No limits on the bunch shape and charge distribution.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PIC-SCHEFF/PICNIC

SCHEFF (1988) [6]

Assume cylindrical symmetry.

Make the mesh at r − z frame.

Solve Poisson equation.

Actually a 2D routine.

PICNIC (1998)[6]

Similar routine with SCHEFF, but use 3D frame.

No limit in symmetry.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PIC-SCHEFF/PICNIC

SCHEFF (1988) [6]

Assume cylindrical symmetry.

Make the mesh at r − z frame.

Solve Poisson equation.

Actually a 2D routine.

PICNIC (1998)[6]

Similar routine with SCHEFF, but use 3D frame.

No limit in symmetry.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PIC-SCHEFF/PICNIC

SCHEFF (1988) [6]

Assume cylindrical symmetry.

Make the mesh at r − z frame.

Solve Poisson equation.

Actually a 2D routine.

PICNIC (1998)[6]

Similar routine with SCHEFF, but use 3D frame.

No limit in symmetry.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PIC-SCHEFF/PICNIC

SCHEFF (1988) [6]

Assume cylindrical symmetry.

Make the mesh at r − z frame.

Solve Poisson equation.

Actually a 2D routine.

PICNIC (1998)[6]

Similar routine with SCHEFF, but use 3D frame.

No limit in symmetry.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PIC-SCHEFF/PICNIC

SCHEFF (1988) [6]

Assume cylindrical symmetry.

Make the mesh at r − z frame.

Solve Poisson equation.

Actually a 2D routine.

PICNIC (1998)[6]

Similar routine with SCHEFF, but use 3D frame.

No limit in symmetry.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PIC-SCHEFF/PICNIC

SCHEFF (1988) [6]

Assume cylindrical symmetry.

Make the mesh at r − z frame.

Solve Poisson equation.

Actually a 2D routine.

PICNIC (1998)[6]

Similar routine with SCHEFF, but use 3D frame.

No limit in symmetry.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PIC-SCHEFF/PICNIC

SCHEFF (1988) [6]

Assume cylindrical symmetry.

Make the mesh at r − z frame.

Solve Poisson equation.

Actually a 2D routine.

PICNIC (1998)[6]

Similar routine with SCHEFF, but use 3D frame.

No limit in symmetry.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PIC-GPT

The routine used in the General Particle Tracer (GPT)(2004)[7]

Nonequidistant 3D mesh.

Multigrid Poisson solver adapted for nonequidistant meshes.

Poisson solvers on meshes with high aspect ratio.

Track millions of particles in a PC.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PIC-GPT

The routine used in the General Particle Tracer (GPT)(2004)[7]

Nonequidistant 3D mesh.

Multigrid Poisson solver adapted for nonequidistant meshes.

Poisson solvers on meshes with high aspect ratio.

Track millions of particles in a PC.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PIC-GPT

The routine used in the General Particle Tracer (GPT)(2004)[7]

Nonequidistant 3D mesh.

Multigrid Poisson solver adapted for nonequidistant meshes.

Poisson solvers on meshes with high aspect ratio.

Track millions of particles in a PC.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PIC-GPT

The routine used in the General Particle Tracer (GPT)(2004)[7]

Nonequidistant 3D mesh.

Multigrid Poisson solver adapted for nonequidistant meshes.

Poisson solvers on meshes with high aspect ratio.

Track millions of particles in a PC.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

PIC-GPT

The routine used in the General Particle Tracer (GPT)(2004)[7]

Nonequidistant 3D mesh.

Multigrid Poisson solver adapted for nonequidistant meshes.

Poisson solvers on meshes with high aspect ratio.

Track millions of particles in a PC.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

Summary

PPI

Find the particle density distribution.Integrate the field.

PIC

Make a proper mesh and assign the charges on it.Poisson Solver.

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

Questions

Which side are we going to stand on?

What can we do better?

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

Selected References I

P. Lapostolle, etl., A modified space charge routine for highintensity bunched beams, NIM A 379 (1996) p. 21-40

M. Martini, M. Prome, Computer studies of beam dynamics ina proton linear accelerator with space charge, ParticleAccelerators, Vol. 2 (1971) p. 289-299

R. W. Garnett, T. P. Wangler, Space-charge calculation forbunched beams with 3-D ellipsoidal symmetry, IEEE PACConf., San Francisco (1991) p. 330

P. Lapostolle, etl., A new approach to space charge for linacbeam dynamics codes, Proc. of the XVIII International LinearAccelerator Conf., Geneva, 1996

D. L. Bruhwiler, M. F. Reusch, High-order optics with spacecharge: the TOPKARK code, AIP Conf. Proc. 297, New York,1994, p. 524-531

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines

Selected References II

N. Pichoff, etl., Simulation results with an alternate 3D spacecharge routine, PICNIC, Pro. of the 1998 Linac conf., Chicago,(1998)

G. Poplau, etl., Multigrid Algorithms for the fast calculation ofspace-charge effects in accelerator design, IEEE Transactionson magnetics, Vol. 40, No. 2, (2004)

He Zhang A Glimpse of The Current Space Charge Effects Calculation Routines