# Presentation: 472501

## Front End Simulation, Recent Results

***Slava Aseev***
*October 19, 2006*

## 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*

## 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**

## Equations

**The set of equations used for the step-by-step integration:**

**where**

## 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 **

## 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.**

## 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**

## Radio Frequency Quadrupole Accelerator

**5 different sections:**
- Input radial matcher
- Input transition cell
- Regular cells
- Output transition cell
- Output radial matcher

##                               REGULAR    CELL

- EMS 3D geometry of the regular cell

- The  regular cell shape

- The 8-term potential expansion of the regular cell

## Multipole components of the regular cell field expansion.

-                 R0=0.34 cm, L=3.3768 cm, m=2

|  | GST EMS[1]+TRACK
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.

## Entrance and exit transition cells: transition from zero modulation to finite modulation

**The distance from the axis to electrodes of th exit transient cell**.

**The  entrance transition cell shape**

**The  exit  transition cell shape**

**Electric field distribution in **
**the transition cell. **

## Entrance and exit radial matcher sections

-  **Vane profiles of the entrance RMS**

**Cut out view of the entrance  RMS vanes**

**. Cut out view of the exit  RMS vanes**

** ****Vane profiles of the exit RMS**

## Field distribution in the end regions (radial matchers)

**The  potential expansion of the exit RMS**

**The distance from the axis to electrodes of the exit RMS**.

**Analytical and computer simulated falloff functions.**** **

## Final simulations

## Phase space plots

## Verification and improvement of space charge calculations: problem formulation

## 2D Space Charge Verification

## Electric field

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

**Here h****i**** is a mesh size and r****i**** is a rms beam size, i=x,y,z**

**Fluctuations of the electric field**

**Recommendation**

**a)**

## Mesh size variation

**Peculiarity of the electric field**** **

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

**Recommendations**

- a)
- b)         0.25<hi /ri <0.5

## 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

## 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**

## Transport matrix calculations

- TRACK coordinates

- TRACE3D and TRANSPORT coordinates

- CANONICAL coordinates

- First order matrix transformation

- COSY, GIOS and more...

## Matrix calculation

***Matrix calculation***

** **

## Matrix calculation: Bending magnet

-                    COSY            TRACK          TRANSPORT
-  1 11       -0.305E+00     -0.287E+00       -0.308E+00
-  1 12        0.672E+00      0.670E+00        0.675E+00
-  1 22        0.155E+00      0.157E+00        0.159E+00
-  1 33        0.253E+00      0.110E+00         0.309E-02
-  1 34       -0.419E+00     -0.422E+00        -0.510E-01
-  1 44       -0.636E+00     -0.634E+00       -0.683E+00
-  1 16        0.414E+00      0.416E+00        0.422E+00
-  1 26       -0.221E+00      0.187E+00        0.181E+00
-  1 66       -0.183E+00      -0.182E+00      -0.123E+00
-  2 11        -0.686E-01      -0.356E-01       -0.692E-01
-  2 12        -0.662E-01      -0.333E-01       -0.653E-01
-  2 22       -0.493E+00     -0.477E+00       -0.498E+00
-  2 33       -0.933E+00     -0.108E+01       -0.103E-01
-  2 34         0.571E-01     -0.382E-01        -0.556E-02
-  2 44       -0.348E+00     -0.448E+00       -0.347E+00
-  2 16        0.129E+00      0.428E+00        0.416E+00
-  2 26        -0.990E-01      -0.888E-01       -0.985E-01
-  2 66       -0.194E+00      0.462E+00       -0.332E+00
-  3 13       -0.762E+00     -0.797E+00       -0.784E+00
-  3 23       -0.159E+01     -0.158E+01       -0.174E+01
-  3 14        0.294E+00      0.299E+00         0.207E+01
-  3 24        0.141E+00      0.140E+00        0.978E+00
-  3 36        0.349E+00      0.345E+00        0.482E+00
-  3 46      -0.104E+00      0.280E+00         0.354E+01

-            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

- 1st order transformation

- 2nd order transformation

##   New elements:  Electrostatic chopper

***  ******New elements:  Electrostatic chopper***

**Side  view **

**Top  view **

- An inter electrode voltage is defined as *V=U(x,y,z)*f(t)*, where *U(x,y,z)*
- is  3D electrostatic field between plates and *f(t)* is user defined function

## New elements: Accelerating  column

**Cut out view of the accelerating  column**

## 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

## New elements: Grid-less four harmonic buncher

**Cat out view of the buncher**

**Electric field along the buncher axis**

**Longitudinal phase space transformation**

## 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.**