Front End Simulation, Recent Results

1
Front End Simulation, Recent Results

• Slava Aseev
• October 19, 2006

2
Content

• TRACK General Beam Dynamics Simulation Code
• RFQ design and simulations
• Design of the input and output radial matchers
• 8-term potential
• 3D fields in the end regions
• Transition cells
• Recent updates of the TRACK code
• Improvement of space charge calculations
• New elements supported by the TRACK
• Matrix calculation
• Quasi-periodical channels
• Bending magnets

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TRACK functions

• Track multi-component heavy-ion beams
• End-to-end simulation from ion source to target
• Wide range of electromagnetic elements with 3D
  fields
• Treat interaction of heavy-ion beams with matter
• Error simulation for all elements
• Beam loss analysis with exact location of
  particle loss
• Fitting and optimization is partly supported

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Equations
The set of equations used for the step-by-step
integration
where
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Fields

• Depending on the geometry and the type of the
  ion-optics device,
• external fields can be defined as
• 3D tables of and in
• 2D tables in for axial symmetric
  elements
• 2D tables of in the median plane
• for rectangular dipole magnets
• 4) The fringe field fall-off for dipole and
  multipole elements is
• described by a six-parameter Enge function

where D is the full element gap
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Space Charge fields

• Solving Poisson equation for multi-component
  heavy-ion beams.
• The charge distribution is defined on a
  rectangular grid using the cloud-in-cell
  method.
• The code calculates both 2D (for DC beams) and
  3D (for bunched beams) space charge fields.
• The 3D Poisson equation is solved with
  rectangular boundary conditions in the transverse
  direction and periodic conditions along the beam
  direction.

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General Description Supported elements

• Any type of RF resonator (3D fields), DTL, CCL
• Static ion-optics devices (3D fields)
• Radio-Frequency Quadrupoles
• Solenoids with fringe fields
• Bending magnets with fringe fields
• Electrostatic and magnetic multipoles
• Multi-harmonic bunchers
• Axial-symmetric electrostatic lenses
• Entrance and exit of HV decks
• Accelerating tubes with DC voltage
• Transverse beam steering elements
• Stripping foils or film
• Horizontal and vertical jaw slits
• Beam correctors
• Combined static and electromagnetic fields

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Radio Frequency Quadrupole Accelerator

• 5 different sections
• Input radial matcher
• Input transition cell
• Regular cells
• Output transition cell
• Output radial matcher

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REGULAR CELL
EMS 3D geometry of the regular cell
The regular cell shape
The 8-term potential expansion of the regular
cell
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Multipole components of the regular cell field
expansion. R00.34 cm, L3.3768
cm, m2
GST EMS1TRACK Fourier analysis Crandall 2 Surface integration DESRFQ 3 Least square fit
A01 0.949 0.941 0.951
A03 0.019 0.021 0.015
A10 0.602 0.601 0.602
A12I4(kR0) 0.056 0.063 0.056
A21 I2(2kR0) -0.019 -0.014 -0.020
A23 I6(2kR0) -0.019 -0.007 -0.020
A30 I0(3kR0) -0.011 -0.010 -0.011
A32 I4(3kR0) -0.010 0.003 -0.009
1. CST Electromagnetic Studio, User Manual
Version 2.0, January 2004, CST GmbH,
Darmstadt, Germany 2. K.R. Crandall. LANL
report, LA-9695-MS, UC-28, April 19A.A. 3. A.A.
Kolomiets. The code DESRFQ, ITEP/ANL, Technical
note, 2005.
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Entrance and exit transition cells transition
from zero modulation to finite modulation
The entrance transition cell shape
The exit transition cell shape
Electric field distribution in the transition
cell.
The distance from the axis to electrodes of th
exit transient cell.
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Entrance and exit radial matcher sections
Cut out view of the entrance RMS vanes
Vane profiles of the entrance RMS
Vane profiles of the exit RMS
. Cut out view of the exit RMS vanes


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Field distribution in the end regions (radial
matchers)
The distance from the axis to electrodes of the
exit RMS.
The potential expansion of the exit RMS

Analytical and computer simulated falloff
functions.
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Final simulations
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Phase space plots
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Verification and improvement of space charge
calculations problem formulation
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2D Space Charge Verification
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Electric field

• Typical field as function of distance from the
• bunch center

Fluctuations of the electric field

• Recommendation

a)
Here hi is a mesh size and ri is a rms beam size,
ix,y,z
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Mesh size variation
Peculiarity of the electric field

• Recommendations

• a)
• b) 0.25lthi /ri lt0.5

TRACK checks conditions a) and b) and sends
warning in SCwarning.dat file when this
conditions are defaulted .
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Matrix calculation

• Necessary for beam optimization and matching
• To compare with other beam optics codes
• Use realistic fields (no hard edges)
• Higher-order matrices are necessary for various
  tasks (large momentum spread, magnet
  spectrometers, mass-separation,)
• Method
• Use probe particles to track through the 3D
  external and space charge fields. Define matrices
  in COSY or TRANSPORT notation

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Transport matrix calculations
Probe particles coordinates at the entrance of a
beam channel
Probe particles coordinates at the exit of a
beam channel
Matrix element calculations
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Transport matrix calculations
TRACK coordinates
First order matrix transformation
TRACE3D and TRANSPORT coordinates
CANONICAL coordinates
COSY, GIOS and more
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Matrix calculation
TRACK calculates 1st order matrix wrt canonical
coordinates.

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Matrix calculation Bending magnet
2nd order transformation
1st order transformation
COSY TRACK
TRANSPORT 1 11 -0.305E00 -0.287E00
-0.308E00 1 12 0.672E00
0.670E00 0.675E00 1 22 0.155E00
0.157E00 0.159E00 1 33
0.253E00 0.110E00 0.309E-02 1 34
-0.419E00 -0.422E00 -0.510E-01
1 44 -0.636E00 -0.634E00
-0.683E00 1 16 0.414E00 0.416E00
0.422E00 1 26 -0.221E00
0.187E00 0.181E00 1 66 -0.183E00
-0.182E00 -0.123E00 2 11
-0.686E-01 -0.356E-01 -0.692E-01 2 12
-0.662E-01 -0.333E-01
-0.653E-01 2 22 -0.493E00 -0.477E00
-0.498E00 2 33 -0.933E00
-0.108E01 -0.103E-01 2 34
0.571E-01 -0.382E-01 -0.556E-02 2 44
-0.348E00 -0.448E00 -0.347E00
2 16 0.129E00 0.428E00
0.416E00 2 26 -0.990E-01 -0.888E-01
-0.985E-01 2 66 -0.194E00
0.462E00 -0.332E00 3 13 -0.762E00
-0.797E00 -0.784E00 3 23
-0.159E01 -0.158E01 -0.174E01 3 14
0.294E00 0.299E00 0.207E01
3 24 0.141E00 0.140E00
0.978E00 3 36 0.349E00 0.345E00
0.482E00 3 46 -0.104E00
0.280E00 0.354E01
COSY TRACK TRANSPORT 1 1
0.73243 0.73013 0.73056 1 2
0.81346 0.81030 0.81657 1 6 0.25293
0.25178 0.25440 2 1 -0.57041
-0.57597 -0.57103 2 2 0.73181 0.73042
0.73056 2 6 0.53638 0.53746
0.53913 3 3 0.36111 0.36636 0.35854
3 4 0.77199 0.77010 7.61600 4 3
-1.12330 -1.12416 -0.11442 4 4 0.36784
0.36665 0.35854
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New elements Electrostatic chopper
Side view
Top view
An inter electrode voltage is defined as
VU(x,y,z)f(t), where U(x,y,z) is 3D
electrostatic field between plates and f(t) is
user defined function
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New elements Accelerating column
Cut out view of the accelerating column
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New elements Accelerating column
Input structure file for the TRACK code 1 deck
Vf d R1 nstep 2 deck Vf L R
nstep 3 deck Vf L R nstep 4 deck
Vf L R nstep 5 deck Vf d R1
nstep
Electric field along the accelerating column axis
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New elements Grid-less four harmonic buncher
Cat out view of the buncher
Electric field along the buncher axis
Longitudinal phase space transformation
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Summary

• The code will be available in the web-site in 1-3
  months
• Parallel version is ready and will be available
  soon (Physics Division BD group)
• The Poisson solver is working now in round
  beamline too.
• Problem Manuals and Documentation does not
  describe all available features of the code.
  There is no Getting Started Manual there are
  no systematic examples.