Trapping of Electron Cloud in CESRTA/ILC Quadrupole and Sextupole Magnets L. Wang, SLAC Ecloud 1 Cornell, Otc 8-1, 1 Acknowledgements Thanks Joseph Calvey, Gerry Dugan, Bob Macek, Mark Palmer, Mauro Pivi for helpful discussions and providing valuable data
Outline Introduction Mechanism of electron trapping in a Quadrupole and Sextupole Electron cloud in CESRTA Quadrupole Electron Cloud in ILC Quadpole and Sextupole Summary
3D PIC Program--- CLOUDLAND CLOUDLAND is a complete 3D PIC code (PRST-AB 144) L Program model PIC methods z y x p+ e- a Various magnetic field (dipole ) & Electric field (clearing electrode, ) h l Charge assignment Mesh of chamber 3 1/1/1 Real charge distribution Meshed Charge distribution
Examples of e-cloud distribution in different magnets N=1. 1e1 Field free region N=3. 3e1 1 8 6 Y [mm] 4 - -4-6 -8-1 -1-8 -6-4 - 4 6 8 1 X [mm] Quadrupole 1/1/1 Drift+Solenoid L. Wang Dipole magnet Wiggler magnet 4
Electron in CESRTA Quadrupole (simulation ) 1.5 e (m ) It happens in quadrupole, sextupole, octutpole magnets The electrons has long decay time and can survive a long bunch train gap x 1 1.5 1.5 16 17 18 Time ( s) 19 Electron cloud density evolution in CESRTA Quadrupole 5
Trapping phenomenon--phenomenon---in in quadrupole magnet 3D orbit D orbit Orbit of a trapped photoelectron in normal quadrupole magnet during the train gap (field gradient=.5t/m) 6 Field lines
Trapping mechanism (I) Mirror field trap The motion of the electron in magnetic field can be regarded as the superposition of the gyration motion around the guide center and the motion of the guide center. Adiabatic invariant For periodic motion J pdq cons tan t Field changes slowly Motion of electron in a 4 m J m s d m mirror magnetic field e m is the magnetic moment J m dl m B the gyration and parallel velocity s the Larmor radius 7
Trapping mechanism (II) Beam induced trapping Invariant value of motion Positron bunch m m m W cons tan t 1 m m B const Beam E-field Reflective Points: = Trapping condition trap 1 F Bmax trap FB B Trap factor is constant if no other force (except B force) disturbs the electron and smaller than 1., no trapping Turning points mirror field trapping trap 8 cons tan t 1 at the emission po int
Orbit of the Guiding Center--Center---Longitudinal Longitudinal Motion Longitudinal Velocity of the Guiding Center (Beam direction) Magnetic gradient drift υgrad m B B With normal gradient Bn/RB 3 eb y Centrifugal force drift m R B m Fc n RB RB F B n B υf eb B s RB Beam Effect (EXB drift) z x Example: one electron in Quadrupole: 9
E-cloud in the Quadrupole of CESRTA 1/1/1 Ecloud' 1 Cornell, L.Wang 1
.8 Slow BuildBuild-up x 1 1.6 e (m ).4 Slow build-up:. 1.8 up to 1 turns to reach saturation 1.6 Slow decay during the long train gap 1.4 1. Trapped electrons (~5%) survive from the long gap (1.9 s) 3 x 1 15.5 16 16.5 Time ( s) 17 17.5 1.5 1.5 e (m ) Parameters used for simulation: Bunch length 15 mm Bunch current 1.3 ma Bunch spacing 14 ns Field gradient.517 T/m Peak SEY. Energy at peak SEY 76 ev 1.5 5 1 15 Time ( s) Ecloud build-up in CESRTA Quadrupole
x 1 1.5 e (m ) Evolution of electron cloud during the train gap, frames separated by t=7 ns 3 1.5 1 15.5 1 Evolution of e-cloud during the train gap, t=7ns 16 16.5 17 17.5 18
RFA in CESRTA Quadrupole (see de tail @Joseph Calvey s talk, 8/9/1) ECLOUD`1 October 9, 1 - Cornell University 13
Evolution of electron cloud (example II) Parameters Bunch length 17.4 mm Bunch current 1. ma Bunch spacing 14 ns
Beam current dependence There is a larger electron density for high bunch current (strong dependence) About 3~6% electrons can survive the long gap (1.9 s) There is a larger electron density for a higher magnetic field (weak dependence) 3.5 x 1 G=.5T/m B=.5T 1 4 I=.5mA I=.75mA I=1.mA I=1.5mA I=.mA 3.5 x 1 1 G=.T/m B=T I=.5mA I=.75mA I=1.mA I=1.5mA I=.mA 3.5 3 e (m ) e (m ).5 1.5 1.5 1 1.5.5 5 1 Time (sp) 15 5 1 Time (sp) 15
Slow buildbuild-up 11 5 x 1 11 B=T, II=.5mA =.5 ma G=T/m, 18 b 4 14 3.5 1 (m ) 3 1 e.5 e (m ) G=T/m, B=T, I bi=1.ma =1. ma 16 4.5 8 6 1.5 1 4.5 x 1 5 1 Time (sp) 15 5 1 15 Time (sp) Ecloud build-up with different bunch current (left:.5ma),(right:1.ma) 1/1/1 Ecloud' 1 Cornell, L.Wang 16
a larger electron density for a high magnetic field (sensitive to beam current) More electrons (in percentage) can be trapped in a weak field 5 x 1 4.5 4 I =.5mA 11 b 18 B=.5T B=.T x 1 I =1.mA 11 b 16 /m 14 1 3 e (m ) e (m ) 3.5.5 1.5 1 8 6 1 4.5 5 1 Time (sp) 15 B=.5T B=.T 5 1 15 Time (sp) 1/1/1 Ecloud' 1 Cornell, L.Wang 17
Magnetic field effect 5 x 1 1 5 Average density Center density 4.5 4.5 4 3.5 3.5 (m ) 4 e e (m ) 3.5 1.5 1.5 1 1.5.5 15 T ime ( s) large field gradient g=9.t/m 5 Average density Center density.5 1 1 3 5 x 1 5 1 Time ( 15 s) Lower field gradient g=.5t/m 5
ECLOUD IN THE ILC QUADRUPOLE & SEXTUPOLE 1/1/1 Ecloud' 1 Cornell, L.Wang 19
Photon parameters Average number of photons emitted per unit length per beam particle in the ARCS are:.47 photons/meter/e+ in the ARCS of 3. km ring Photoelectric yield:.1
Build Up Input Parameters for CLOUDLAND ilc-dr 3. Km, 3/6 ns bunch spacing*. Bunch population Nb.1x11 Number of bunches Nb 45 per train Bunch gap Ngap 15 bunches Bunch spacing Lsep[m].9 Bunch length σz [mm] 6 Bunch horizontal size σx [mm].7 Bunch vertical size σy [mm].5 Photoelectron Yield Y.1 Photon rate (e-/e+/m) dn /ds. 47 Antechamber protection %, 9%, 98% Photon Reflectivity R % Max. Secondary Emission Yeld δmax.9~1.4 Energy at Max. SEY Εm [ev] 3 SEY model Cimino-Collins ( ()=.5) *https://wiki.lepp.cornell.edu/ilc/pub/public/dampingrings/webhome/dampingringsfillpatterns.xls
Example: ILC Quadrupole Antechamber protection =98%
Average density 16 1 x 1 x 1 149 8 1 7 3km Ring, 3ns Spacing =.9 3km Ring, 6ns Spacing =1. =1.1 =.9 =1. =1. =1.1 =1.3 =1. =1.4 =1.3 =1.4 5 e ) e (m (m ) 16 1 1 84 3 6 1 4 1 3 4 5 Time (sp) 4 6 Time (sp) 3 ns spacing 8 1
Bunch Spacing effect 11 x 1 3km Ring, =.9 11 x 1 3 e (m ) e (m ) 4 3 1 Quadrupole: Photon Quadrupole: Reflectivity =% Antechamber protection =98% 8 6ns Spacing 3ns Spacing 4 1 4 6 8 1 1 3km Ring, =1.3 x 1 15 e (m ) 1 1 8 6 4 e (m ) slow saturation for 3ns spacing a larger ecloud density for 3ns spacing : 13%( =.9) ~6%( =1.4) 6ns Spacing 3ns Spacing 6 Average density build--up build 4 6 8 1 1 3km Ring, =1. x 1 e (m ) e (m ) 3 6ns Spacing 3ns Spacing 1 6ns Spacing 3ns Spacing 4 6 8 1 1 3km Ring, =1.1 x 1 4 3km Ring, =1. 4 6 8 1 1 3km Ring, =1.4 x 1 1 5 6ns Spacing 3ns Spacing 4 6 8 1 Time (sp) 4 6ns Spacing 3ns Spacing 6 8 1 Time (sp)
Summary of ecloud in ILC Quadropole Peak average density in ILC quadrupole ( 11m) SEY.9 1. 1.1 1. 1.3 1.4 Antechamber protection =% Antechamber protection =9% Antechamber protection =98% 3ns spacing 6ns spacing 3ns spacing 6ns spacing 3ns spacing 6ns spacing 1. 8.4 1.64.7.315.136 1.8 8.7. 1..466.6 13.85 9.41 4.8.38 4.3. 15.74 1.44 8.7 5.5 8.4 5.13 17.5 11.45 13. 8.58 1.8 8.35 19. 1.35 15.8 9.97 15.37 9.7 Peak ecloud density near the beam in ILC quadrupole ( 11m) SEY Antechamber protection =% Antechamber protection =9% 3ns spacing 6ns spacing 3ns spacing 6ns spacing 3ns spacing 6ns spacing.9 1..67.18.11.35. 1. 1.6.9.55.35.135.14 1.1. 1.5 3.5. 4..75 1. 4.4.6 7.5 6. 8.7 6.55 1.3 6.7 3.8 11.5 8.5 1.4 9. 1.4 7.5 4.9 13. 9.5 13.6 9.9 1/1/1 Antechamber protection =98% Ecloud' 1 Cornell, L.Wang 5
Summary of ecloud in ILC Sextupole Peak average density in ILC Sextupole ( 11m) SEY Antechamber protection =% Antechamber protection =9% Antechamber protection =98% 3ns spacing 6ns spacing 3ns spacing 6ns spacing 3ns spacing 6ns spacing.9 11.3 6.4 1.7.5..1 1. >11.8 7.5 1..65..116 1.1 >1.4 7.75 >1.35.73.48.135 1. >13. >8.46 >1.55.94.9.174 1.3 >13.8 >9.3 1.95 1.56.354.33 1.4 14.8 1. 3.3 3.5.65 >. Peak ecloud density near the beam in ILC Sextupole ( 11m) SEY Antechamber protection =% Antechamber protection =9% Antechamber protection =98% 3ns spacing 6ns spacing 3ns spacing 6ns spacing 3ns spacing 6ns spacing.9.55.4.6.5.1.8 1..6.5.8.7.14.1 1.1.7.55.1.85.18.16 1..9.75.145.15.6.5 1.3 1.3.9.4.37.5.75 1.4 1.4 1.1.76 1.14.18 >1. 1/1/1 Ecloud' 1 Cornell, L.Wang 6
Summary and future work A larger number of electrons (3%~7% ) can be trapped and survive a long train gap; there is slow build-up and slow decay. (can explination of the obersevation?see Gerry s talk ) We sysmatically studied the effects of Bunch current, Magnetic field, and bunch spacing Antechamber is effective in reduction of the ecloud density when SEY is small (<=1.); For High SEY, its mitigation effect becomes small becauses the seconaries are dominant. For ILC Quadrupole, there is a larger (a factor.3~1.6) average electron density in 3ns spacing case comapring with 6ns spacing; Benchmark with RFA : need a better model 1/1/1 Ecloud' 1 Cornell, L.Wang Simulation of one section of the ring(multi-magnets effect) 7
Acknowledgements Thanks Joseph Calvey, Gerry Dugan, Bob Macek, Mark Palmer, Pivi Mauro for fruitful discussions and information 1/1/1 Ecloud' 1 Cornell, L.Wang 8
Backup slides 1/1/1 Ecloud' 1 Cornell, L.Wang 9