# Presentation: 270270

## Simulations of VENUS extraction and transport using WARP

- Damon Todd
- May 15, 2008

## Source/Transport Overview

- For ion beam analysis the only optical elements used are a solenoid lens and analyzing dipole

## VENUS simulation approach: simulate two separate sections in Warp

- Simulation of extraction section:

- Simulation of transport section

- 2D slice mode (x,y) simulation method:
- Read particle distribution from extraction simulation
- Solve Laplace for potential on x-y mesh (x’,y’<<1, so treat as infinite in z)
- Move particles using solved field and any applied fields
- Repeat from 2 to end of simulation

- 2D or 3D PIC plasma extraction method :
- Track ions through applied electromagnetic fields, depositing charge density on a system-wide mesh
- Solve Laplace equation for potential on mesh using charge density and electrode voltages
- Update potential by adding a Boltzmann distribution of electrons on
- 	mesh 		 using potential from step 2
- 4. 	Use this new potential as an applied field and repeat from 1 until relaxed
- 5.	Write particle distribution after extraction to a file

- 20-30 kV

- -1 to -5 kV

- 0V

- Plasma

- Beam

- Beam extraction

- Beam transport

## Parameters needed for each section’s simulation

- Necessary parameters for extraction simulation and settings:

- Necessary parameters for transport simulation and settings:

| Puller position, extraction voltage, puller voltage | Measured |
| --- | --- |
| Source magnetic fields | Source fields calculated in Vector Fields and read in as axial, one-dimensional array (sextupole influence on extraction dynamics assumed small) |
| Ion currents (individual and total extracted) | Sum of measured individual ion currents often don’t sum to total extracted current.  Must be scaled (how?) |
| Plasma potential | Plasma potential derived from extracted currents by species and temperature |
| Ion and electron temperatures | Ion/electron temperatures assumed to be ~3eV each |
| Neutralization downstream of puller electrode | Neutralization level measured to be very small ~80 cm after extraction. Zero neutralization assumed in simulation |
| Ion distributions at extraction | Ion distributions for each individual extracted species unknown |

| Source magnetic fields | From Vector Fields and read in as one-dimensional array |
| --- | --- |
| Solenoid lens field | From Vector Fields and read in as one-dimensional array |
| Analyzing dipole field  | Solved in Vector Fields for field on Cartesian mesh.  External C program used once to convert to Frenet-Serret coordinates |
| Neutralization level | Unknown in bend.  Assumed zero throughout |

## How we run Warp extraction simulation

- Extraction python script consists of:
- ~350 lines of code
- 4 primary sections:
- Beam set-up (changed with each use)
- Set Vext, Vpuller, puller position, Te, Ti, Iext, Ilens, and number of particles
- Read external text file with species information
- Mesh set up (usually unchanged)
- Set mesh size (typically 0.25 mm in r and z)
- Define conductors and magnetic fields (never changed)
- Read and scale external file with axial field (1D) of extraction solenoid and solenoid lens
- Run actual plasma extraction simulation (occasionally changed)
- Run a defined number of iterations to relax system
- After relaxed, write particle information at a defined z-location into a binary file

- Plus many additional lines of code to set up simulation that are never changed

## How we run Warp transport simulation

- Transport python script consists of:
- ~170 lines of code
- 4 primary sections:
- Beam set-up (changed with each use)
- Set Blens and species to bend
- Read external binary file with particle information from extraction simulation
- Mesh set up (usually unchanged)
- Set mesh size (typically ~ 0.25 mm)
- Define magnetic fields (never changed)
- Read and scale external file with axial field (1D) of extraction solenoid and solenoid lens
- Read and scale external file with analyzing dipole field
- Move particles through system (rarely changed)
- Move to end of simulaiton and write final particle positions/velocities

- Plus many additional lines of code to set up simulation that are never changed

## Initial distributions for extraction

- What we expected to find:
- To-first order round beams: extraction aperture diameter small (8 mm) relative to resonance zone diameter (~ 80-100 mm)
- First simulations predicted round beams

- What we found when imaging beam He+ beam 80 cm after extraction:

- Boltzmann distributed ions tracked from within resonance zone to extraction aperture had same spatial distribution over extraction aperture for all beams
- This distribution was of constant density across the entire 8 mm-diameter aperture---round, symmetric beams

## Why using field lines alone won’t work

- Extraction Electrode
- ~2.3 T axial

- Biased Disc
- ~3.3 T axial

- 1 tesla (28 GHz) resonance zone

- Assumptions
- Ions primarily follow field lines
- Electrons heated only on field lines with resonance zone crossing
-  get initial conditions from field lines which intersect resonance surface

**Red**: Field line terminates on axial ends of source
**Blue**: Field line terminates on a wall

- 14 cm

- 50 cm

- Plotted field lines →

## Field line distribution at extraction electrode

- Plasma markings on the original VENUS extraction electrode, replaced in early 2005.
- Source aperture has 4 mm radius

- Terminal points of field line tracing through VENUS source fields

- To
- Wall

- To biased
- disc

- Every field line through aperture terminates at biased disc
- Neither ion tracking nor field line tracing produce triangular distribution at aperture

## Biased disc for initial conditions

**2004**

**2007**

- Biased disc is normally operated between -50 and -100 volts relative to source chamber
- Plasma markings on biased disc similar to extraction electrode, but there is also a 0.5 mm deep, 5 mm tall inner triangle
- Inner triangle has what appears to be constant depth and sharp edges
- Believe that this inner triangle is due to sputtering by ions accelerated into biased disc

**AECR**

## Field Lines From Triangle Through VENUS

- Injection

- Extraction

- 14 cm

- Field lines originating at biased disc sputtered triangle produce terminate with a triangular distribution smaller than the aperture at the extraction electrode

## Extraction distribution from biased disc mark

- Injection

- Extraction

- Extraction simulation initial conditions:
- Initialize random, constant density distribution of each ion species on measured triangle
- Give particles Boltzmann distributed energy
- Track particles through applied magnetic field

- M/Q=16.0

- M/Q=4.0

- M/Q=2.0

- Initial conditions need only be generated once

## An aside: the triangle

- What to do for a system with an unsputtered biased disc or none at all?
- Track field lines from the biased disc to the extraction aperture to find field lines which pass through aperture
- Resulting triangle seems to give good approximation of shape of a sputtered triangle

- Mapping of biased disc positions to radial location through extraction aperture for VENUS following field lines.  Triangle drawn in black is the measured size of the VENUS triangular sputter mark on biased disc

- Radial position at extraction aperture [mm]

- 0

- 4

- Xbiased disc [mm]

- Biased disc

- Extraction aperature

- Radius [mm]

## 3D Simulation of Extracted Triangular Beams

- Extracted He+ beam, 20 cm after aperture
- Mesh artifacts appear due to too coarse of a mesh

## Comparison of 2D and 3D Extraction

- Mesh artifacts show up in three-dimensional mesh
- To rid simulations of these require much greater mesh densities: rather than the switch from 2D to 3D being an increase in necessary mesh points from Nr*Nz to Nr2*Nz, it increases as (αNr)2*Nz, where the typical α is 5 to 10
- 3D simulations also require more particles for the greater mesh densities

**Three Dimensional simulation**

**Two Dimensional simulation**

- Round beam extraction at z=20 cm

## Compromise: Use 2D Model to Simulate 3D

- Using solution of potential from a 2D (r,z) extraction simulation as an applied field to track asymmetric 3D initial distribtion gives an extracted beams with similar properties to 3D beam
- Advantage: significant reduction in mesh cells allows for greater simulation statistics

## Using the initial, triangular distribution

- 3D simulation:
- Capable of correctly simulating asymmetric extraction
- Computationally expensive: Number of necessary mesh points increases (25 to 100)*Nr2 rather than just Nr2
- Large number of mesh points limits number of particles that can be simulated
- Simulations are very slow
- Parallel extraction model doesn’t yet exist, so multigridding is necessary (easy to make mistakes)

- 2D simulation:
- Required mesh densities much lower than 3D
- Axially symmetric simulations require much fewer particle densities so can run considerably faster
- Can’t simulate triangular extraction

- A compromise -> 2D+ simulation method:
- Use appropriately chosen, cylindrically symmetric initial distribution and simulate extraction in 2D (we have been using circular beam with same total current and current density as triangle)
- Write solved potential from this simulation to a file
- Run second extraction simulation where written potential from previous is read in as an applied field for a one-pass tracking simulation of ions using an initial triangular distribution
- Write asymmetric tracked particle distribution to file and use this as the initial conditions for the transport simulation

## How we run 2+ dimensional Warp extraction simulation

- 2+ dimensional extraction scripts consist of:
- ~350 lines of code
- 4 primary sections:
- Beam set-up (changed with each use)
- Set Vext, Vpuller, puller position, Te, Ti, Bext, and Blens
- Read external text file with species information
- Set “equivalent” symmetric simulated beam size
- Read in initial triangular particle distribution
- Mesh set up (usually unchanged)
- Set mesh size
- Define conductors and magnetic fields (never changed)
- Read and scale external file with axial field (1D) of extraction solenoid and solenoid lens
- Read in relaxed potential as applied field
- Run actual plasma extraction simulation (occasionally changed)
- Run a defined number of iterations to relax system
- After relaxed, write relaxed potential to file
- Track particles through applied fields and write final positions/velocities to file for use in transport simulation

- Two extraction nearly-identical simulation scripts are necessary when running the 2+ dimensional simulation:
- 	1. Symmetric simulation which runs symmetric beam and relaxes solution
- 	2. Triangular simulation which initializes triangular distribution to run through relaxed field from 1.

## Simulation of Oxygen Beam Extraction and Transport

- Simulation

- Experiment

- Simulation

- Experiment

- Experiment

- Experimentally Measured Spectrum

## Comparison of C4+ beam shape

- Experiment

- Simulation

## Where we are and where we need to go

- We are using Warp to simulate both extraction and transport from VENUS by breaking the system into two separate sections
- Developed a method of initializing extraction simulations based on the biased disc sputter marks
- We have a method of simulating asymmetric beam extraction using the axially symmetric extraction model giving us much faster simulations and much better particle statistics than the 3D extraction model
- Simulations produce beams with distributions sharing similar properties with experimental measurement (e.g. hollowness) without an exotic initialization scheme

- Where we are

- Where we need to go

- Systematic study of simulation effects when varying model parameters not easily measured experimentally. Adjust parameters such as radial current distribution in initial 2D extraction simulations and level of neutralization along beam transport line to improve agreement with experiment

## Beam Neutralization Along Beam Line

- Beam End View

- Velocity of ejected ions depends on level of beam neutralization

## Field lines through 18 GHz Resonance Zone

- All field lines that terminate on the ends of the plasma pass through both resonance zones
- Only some of the field lines that terminate through the wall pass through the 18 GHz (0.64 tesla) zone

- 0.64 T (18 GHz) resonance zone

## Extraction elecrode

- Red points pass through both resonance zones
- Blue points strike wall but pass through 28 GHz resonance zone
- Green points also strike wall, but pass through both the 18 and 28 GHz resonance zones

- Triangular structure larger than aperture.  Analysis of distribution of field lines within aperture gives constant density distribution

## Beam Analysis at Harp

- 600 μA He+ beam analysis

- Source Sextupole Off

- Normal Source Operation (Sextupole On)

- Solenoid
- Lens

- Vertical

- Horizontal

- Beam
- Extraction