# Presentation: 271234

## Microscopic Phenomenological Model

- for the
- Secondary Emission Process
- M. Furman and M. Pivi
- LBNL

*ECLOUD-02 Workshop*
*CERN, April 15-18, 2002*

##  Motivation

-  Definition of the model
-  Fits to Cu and St. St. data
-  Applications
-  time dependence of the electron-cloud power deposition in an LHC arc dipole
-  time dependence of the electron cloud dissipation in the PSR following extraction of the beam
-  Conclusions

## Our main focus: 

-  Understand in detail the effects of:
-  details of the secondary electron yield (SEY)
-  details of the secondary electron energy spectrum
-  Simulations started in 1995 (with G. Lambertson):
-  PEP-II, LHC, APS, SPS, ...
-  main input: SEY () and secondary energy spectrum (d/dE)
-  obtained from lab measurements (R. Kirby, SLAC; N. Hilleret, CERN)
-  also books by Bruining, Redhead et al, and various articles in J. Appl. Phys. and other journals
-  SEY model in the simulation originally developed in 1995
-  several refinements over past 1-1/2 years (M. Pivi)
-  some errors fixed (no major effect on results)

## Details of the model: 

- _Details of the model_:
-  event-by-event simulation(*)
-  event=one electron-wall collision
-  instantaneous generation of n secondaries (or absorption)
-  include E0 and 0 dependence
-  constraints for any single event:
-  Ek≤E0, k=1,2,...,n
-  k Ek≤E0
-  constraints for the average over many events:
-   nPn=(E0,0)=input data
-  dE=input data

- ____________
- (*) In our ECE simulation code, *all* macroparticles have the same charge (and mass)

## Slide 5

## Basic macroscopic phenomenology

- _Basic macroscopic phenomenology_

- SEY:

- Cumulative energy spectrum:
-    apply a retarding voltage E=eV

- Retarding-voltage spectrum:

- What we need for an event-by-event simulation is:

- (steady-state currents)

## From

- obtain any macroscopic quantity:

- We have constructed a phenomenological model for

-  based as much as possible on data for  and d/dE
-  not unique (use simplest assumptions whenever data is not available)
-  many adjustable parameters, fixed by fitting  and d/dE to data
-  satisfies the single-event constraints
-  Ek≤E0, k=1,2,...,n
-  k Ek≤E0
-  still evolving
-  good agreement with data (by construction)
-  some shortcomings

## Ignore for now the emission-angle distribution (ie., integrate over angles)

- Ignore for now the emission-angle distribution (*ie*., integrate over angles)

- Three components of emitted electrons:
- backscattered:
- rediffused:
- true secondaries:

## Slide 9

## Exclusion assumption:

- _Exclusion assumption:_
-  if n=1, electron can be either backscattered, rediffused or true secondary
-  if n≥2, electron can only be true secondary

- This is a simplifying assumption:
-  allows to easily extract the energy distribution functions fn(E) directly from the energy spectrum d/dE
-  no fundamental physical reason
-  consistent with data on d/dE for E0>50 eV or so, but not implied by it

## Typical secondary emitted-electrons energy spectrum

- true sec.

- back-scattered
- elastic

- re-diffused

- component

## Algorithm:

- 1. When an electron hits the wall, record E0 and 0
- 2. Compute e(E0,0), r(E0,0) and ts(E0,0)
- 3. Compute Pn, n=1,2,...,M      (typically, M=10)
- 4. Generate a random integer n[0,M] with probability distribution {Pn}
- 5. If n=0, electron got absorbed; continue with next incident electron
- 6. If n=1, generate its energy E with probability distribution f1e(E)+f1r(E)+f1ts(E) such that
- 7. If n≥2, generate their energies Ek with probability distribution fnts(Ek) such             that
- 8. Generate the emission angles (k,k) for k=1,2,...,n
- 9. Continue with next incident electron

## Fits to data:

-  Copper (data courtesy N. Hilleret, CERN)
-  sample: chemically cleaned but not vacuum-baked *in situ*
-  Stainless steel (data courtesy R. Kirby, SLAC)
-  sample: SLAC standard 304 rolled sheet, chemically etched and passivated but not conditioned

## Slide 14

## Slide 15

## NOTE: rediffused+backscattered~50%

- (assuming low-energy cutoff=50 eV)

## NOTE: rediffused+backscattered~5%

- (assuming low-energy cutoff=50 eV)

## Slide 18

## Slide 19

## Current parameter values from fits to data

## Q: is the electron emitted spectrum Maxwellian? 

- A: only approximately.

- Fits to data, however, imply *p*n~1.8–5, depending on *n* and material

- definition of Maxwellian spectrum:

## Applications:

- (1) time dependence of the electron-cloud power deposition in LHC arc dipole:
- 	 simulate injection of a 15-bunch train into an empty chamber;
-  sensitivity to relative ratio of backscattered, rediffused and true secondaries
-  sensitivity to (0)
- (2) time dependence of the electron cloud dissipation following extraction of the PSR beam

## backscattered and rediffused electrons

- artificially suppressed (true secondaries only)

## Slide 24

## Slide 25

## (detailed view for copper only)

## Slide 27

## Slide 28

## Slide 29

## Dissipation of the electron cloud upon extraction of the PSR beam (data courtesy R. Macek)

- Macek-Bowman data

- wall current
- (a.u.)

## Conclusions:

-  constructed phenomenological model for secondary emission process
-  consistent with data on (E0) and d/dE (by construction)
-  probabilities Pn calculated self-consistently (ie., (E0) and d/dE are reproduced  	from the Pn’s)
-  still evolving; not enough detailed data to pin down all parameters
-  _Applications_:
-  power deposition in LHC dipoles exhibits a sensitivity to details of the secondary emission spectrum (relative ratio of backscattered, rediffused and true secondaries)
-  however, this sensitivity may be less pronounced when in steady state
-  also sensitivity to (0) (not new)
-  for PSR, infer eff(0)=0.5-0.6 from measured data on dissipation of the electron cloud following extraction

## Sample comparison of simulation vs. measurements at the APS