beam vacuum interactions ii - cern

Beam vacuum interactions II

Oswald Gröbner

O. Gröbner, CERN-Vauum group (ret.)

Present address: Schmiedgasse 5, 6020 Innsbruck, Austria

E-mail: [email protected]@cern.ch

Vacuum in Accelerators 16-24 May 2006, Platja d’Aro, Spain

O. Gröbner Beam vacuum interactions II 2

Specific ionisation of the residual gas

Ionisation of the residual gas by the high energybeam

σp is the ionisation cross section

€

I p =σ pPgaskT IbeamIonisation cross-sections for

high energy particles in units of10-18 cm2

Gas 26 GeV 7 TeVH2 0.22 0.37He 0.23 0.38CH4 1.2 2.1CO 1.0 1.8A 1.1 2.0CO2 1.6 2.8

e.g. LHC arc: Ip~ 20 nA/m atnominal current and density(1015 H2/m3)


Power loss by nuclear scattering

Particles lost by nuclear scattering along the arcs of amachine can not be collimated and their losses occuruniformly distributed around the arcs

€

P(w /m)=1cIEτ

=0.93 I(A)E(TeV )τ(h)

LHC design requires a nuclear-scattering life time of ~ 100h

LHC -> 0.1 W/m for two beams at ultimate current requiredgas density equivalent to 1015 H2/m3

Each W at 1.9 K ~ 500 W at RT (Ph.L. lecture)


Space charge potential of the beam

Line density (particles/m), totalcurrent I

Circular, concentric geometry, beamwith uniform charge and radius a .Electric field follows from Gauss law

€

λ =Ieβc

€

ε r( ) =eλ2πε0

ra2

r ≤ a

€

ε r( ) =eλ2πε0

1r

r ≥ a

Integrating the field gives the potentialin the centre of the beam

€

Vb =eλ2πε0

12

+ lnrpa

ISR: I = 20 A, rp = 0.08 m a = 0.01 mElectrons remain trappedin the potential well


Record book: the largest ionisation gaugeIonising beam current 10 - 60 AGauge length 2 x 1kmCurrent resolution 20 pA1-300 collectors & true <P> seen by beam

Further reading: ISR clearing current monitoring system, O. Grobner, P. Strubin, PAC1977_1376

The integrated pressure aroundthe whole machine requires asingle electrode only

!! LHC has a bunched beam therefore this system can not be used.

10-12


Beam space charge neutralisation

The neutralisation factor is defined asNb is the number of beam particles ni is the neutralising charge, i.e. electrons trapped ina proton beam, or positive ions trapped in an electronor antiproton beam.Production rate (s-1 m-1) depends on gas density

€

η =niNb

≤1

Equilibrium neutralisation

€

ηequ =RpRc

Trapped charges neutralise the beam space charge and cause atune shift and beam instabilities

€

Rp = βcngσ i

The clearing rate Rc depends on the specific mechanism

prop. to pressure!


Space charge neutralisation tune shift

Space charge due toneutralisation changesthe focussing

€

k(s) =e

γm0c2

dr E

dx

€

ΔQ =14π

β(s)k(s)ds∫

€

di =12πR

Nbπa2

η

€

ΔQ ~ 20ηγ

For most accelerators a few 10-3

neutralisation are harmful

€

r E xdx

=Ib

2πε0βc1a2

€

r F =

r F e(

1γ2−η)

€

ΔQ = −r0R βxIbeβc

1a2ηγ

= r0RQx

Nb

2πa2ηγ

For ISR->


Ion stability in a bunched beamPositive ions can be trapped in a bunchedelectron beam-> successive bunches givekicks to the ionsα attractive kick given by a bunch, nnumber of bunches, T revolution time

€

α =4cr0

b(a+b)1ANb

n=2cr0a2

1ANb

nThe ion motion is stable if

€

−2 <Tr(M ) < 2

€

y˙ y

after= M

y˙ y

before

Drift * Kick

€

M =1 t0 1

1 0α 1

€

−1< (1−α T2n) <1 ⇒αc =

4nT

Ions with masses larger than acritical mass Ac accumulate

€

Ac =cr02a2

Nb

nTn

= πr0RNb

a2n2LHC: Ac ~10 -> electrons are ejectedLEP: 4 intense e- bunches Ac > 200 e- rings all require a ‘clearing gap’


Proton-electron instabilityElectrons oscillate in the potentialwell of protons -> excite protons tooscillate: coupled oscillators

e-p oscillations observed in the ISR and in manyaccelerators: ~ 80 MHz -> beam size increases!

Spectral lines -> harmonics of the revolution frequency.

With bad vacuum electron oscillations cover a widefrequency range

€

˙ ̇ z p + (Q2 +Qp2 )ω2zp = Qp

2ω2z e

€

˙ ̇ z e +Qe2ω2ze = Qe

2ω2z p2

€

Qe2ω2 =

Nprec2

πRa2

€

Qp2ω2 =

rpc2Ne

γπRa2Bouncefrequencies:

€

Qp =(n −Qe )

2 −Q2

2 Qe(n −Qe )Stability limit forprotons a few %neutralisation

Single instability ~20 ms


Coulomb heating of trapped electronsMultiple collisions with the beam ->beam heating

Momentum transfer depends on thevelocity and the charge, not on themass of the beam particle

Physical limits on b: maximumallowed energy transfer and thecondition that the electron can beconsidered stationary.

Energy transfer is inverselyproportional to the mass of the particle-> for ions heating is very inefficient

€

ΔE(b) =(Δp)2

2m=2mc2

β2re2

b2

€

ΔEmax ⇒ bmin =re2

β2γ

z, M

bv

e, m

€

Δp(b) = eE(t)dt−∞

+∞

∫ =2mcβ

reb


Electron heating by multiple scattering (ISR)

€

d2Nb(r)dt

=Nb

2πRπa2βc 2πrdr

€

ρ =Nb

2πRπa2

€

dEdt

=4re2mc2Ibea2

ln rmaxrmin

Numerical example ISR:I = 20 A, R= 150 m, a = 0.01 mRmax = vacuum chamber = 0.04mγ= 28. beam potential ~ 2kVHeating rate ~ 680 eV/sClearing rate ~0.3/s

€

ΔE(b) =2mc2

β2re2

b2

€

d2E(r)dt

=2re2mc2

βcNbRπa2

drr

€

Ib = eNbc2πR

€

bmin =reβ2γ

r

dr

Beam section


Electron clearing by a bunched beam

Electrons have 1/2000 the mass of aproton -> are not trapped in abunched proton and positron beam

ISR: e-cloud build-up in asection with bad vacuum andwithout electrostatic clearingelectrodes.

Bunching the ISR beamclears electrons

10 s


Ion impact energy

Bunched beams: heavy ionsintegrate the passage of manybunches and see an averagefield.Light ions gain a more energy,since they see the peak field.Final energy depends on theinitial position in the beam

Ions are repelled by the positive space charge and hit the wall with asignificant energy -> several keV

Ion energy in LHCM = 2, 4, 28, 44, 500


Density increase by ionsIons trapped in the beam contribute to the gas density

€

db =Ibe

1βca2π

The ion density for a given degreeof neutralisation will add to theneutral gas density

The beam density and the residualgas densities add up to give €

di =ηdb

€

dg =PgkT

€

dtotal =ηIbe

1βca2π

+PgkT

e- ring: Ib= 1Aa = 0.002mPg = 10-7 Pa dg ~ 2.4 1013 m-3

db ~ 1.6 1015 m-3 few% neutralisationwill be a dominatingcontribution


Dust particle trappingTrapping of ‘macroscopic’ (<10-6 m size) dust particles has caused

problems in several machines with negative beams:Antiproton accumulator, e- ring in HERA and Super-ACO

Dust charges positively due to loss of electrons ~106 chargesDust can remain trapped in the intense beam and cause lifetime

degradationRemedies are fast beam shaking to eject the ‘slow’ dust from the

potential wellOrigin of dust is not clear but evidence points to integrated sputter

ions pumps in HERA e- ring and to ion pumps mounted abovethe beam in LEP

HERA dust problem solved by replacing IP’s with linear NEGpumps.


Electron cloud

δ(E,φ)

Y(E,φ)

γ

Reflection

Secondary electrons

Synchrotron radiationY(E,φ) photoelectric yieldδ(E,φ) second. electron YSecond. electron energyresidual gas ionization

Photon reflectivityBeam pipe shapeBunch intensity and spacingExternal fields (magnetic,electric, space charge)

Key parameters


Electron cloud multipacting

€

E(r) =λ

2πε0r

€

Δp = eEτ =e2nb2πε0cr

€

Lbb = ctbb€

Δv =Δpm

= 2crenbr

€

2rpv

= tbb

The electric field of a bunchwith the line density λ and β∼1

Momentum transfer by thebunch is independent on thebunch length τ

Velocity gained by an electron

Condition for wall-to-wall multipacting

€

λ =enbβcτ

rpBeam pipe

With

€

nb =rp2

reLbb particles per bunch

>> can occur also in a beam transfer line with a single pass


Gaussian beamGaussian density distribution

€

E(r) = const1− e−( r rb

)2

r

€

m ˙ ̇ r = eE r( )Electrons move during the kickof a bunchIntegrating the equation ofmotion gives r(t), the velocityand energy

€

ΔW =m ˙ r τ( )2

2=

2mc2

ere

2 nbr

2

Energy (eV) of a stationary(red) and moving electronversus the initial radial positionfor different bunch length

0.1 ns

0.25 ns

0.5 ns


Effect of a dipole magnetic field

SR photons -> median planePhotoelectrons suppressed bythe magnetic field.

Reflected photons reach top andbottom of the beam pipe ->Low photon reflectivity is desirableto reduce photoelectrons which canmove freely along the field lines.

Cyclotron oscillations/bunch ~120Cyclotron radius ~ 6 µm for 200 eVF force by the proton bunch

B

φF

Electron

ElectronBeam


Electron cloud in a dipole beam screen

Energy vrs. horizontal position Yield [energy (eV)]

Yield for different nb

35

1130

Horizontal multipactingrange

Bunch intensities1010 per bunch


Beam screen in an LHC dipoleELECTRON CLOUD SCREEN (addition)

BANDS OF CLOUD ELECTRONS

Strip with saw tooth


Pressure increase due to BIMGas load, Qcloud is related to the power deposited bythe electrons, Pcloud, to the molecular desorption yield,ηe and to the average energy of the electrons in thecloud, <Ecloud>.

€

Qcloud = k ηePcloud< Ecloud>

0

1

2

3

4

5

6

7

8

9

0.0E+00 1.0E+12 2.0E+12 3.0E+12 4.0E+12 5.0E+12 6.0E+12 7.0E+12

Number of protons

Rel

ativ

e P

mb

ar in

crea

se

VG50660 Dipole magnetic fieldVG51880 No magnetic field

Courtesy M. Jimenez

LHC cooling limit: Pcloud ~ 1 W/m -> 10-6 mbar l/s/m


Reduction of BIM with beam dose

MAX SEY vs photon dose at EPACritical energy 194 eV

0.00

0.50

1.00

1.50

2.00

2.50

1.E+18 1.E+19 1.E+20 1.E+21 1.E+22 1.E+23 1.E+24

Photon dose (ph/m)

100 V-45 V350 V

Sample at - 45 V

Sample at + 100 V

Sample at + 350 V

~ 1 year of nominal LHC operation

Beam scrubbing reducesthe secondary electronyield and pressure rise

y = 12e-0.9 x

1

10

100

0:00 12:00 24:00 36:00 48:00 60:00

Running hours

Rel

ativ

e P

incr

ease

VG50660

VG52260

y = 10e-0.9 x

Gauges placed between dipoles

Running hours SPS

Photon dose in EPA

Courtesy V.Baglin

Courtesy M. Jimenez


Suppression of secondary electronsTrue secondary electronsreflected electrons E < 50 eVare trapped by a weaksolenoid field.

Electron energy (eV)Between bunches, low energyelectrons are confined close tothe vacuum chamber walls by aweak external solenoid field

R. Cimino et al. Phys.Rev.Lett. 93 (2004)014801/1-4


Solenoid field in drift chambers

€

r =mveB

€

r(m) =2me E(eV )B(T )€

tcycl = 2π meB

€

twall−wall ~πmeB

< bunch spacing

Energy (eV)

Radius (m) at 30 Gauss

r

Field (Gauss)

Trajectory time (ns)

LHC

KEKB


KEKBDrift chambers with solenoids

Solenoids in quadrupoles are ineffective -> would require amuch higher field


Beam pipe with antechamber

C-magnet

S.R.

Synchrotron radiation iscaptured in the ante-chamber section.

C-magnet aroundantechamber trapsphotoelectrons.

Residual gas ionisation inthe beam duct remains asan electron source


KEKB (Y. Suetsugu)


Surface coating (A. Rossi)

A. Rossi, presented at E-Cloud 04

The Secondary Electron Yield of TiZr andTiZrV NEG thin film coatings

• Normal PE (Primary Electrons) angle of incidence, 60 eV to 3 keV. PE ~5·10-9 A, pulsed, giving a total dose < 10-8 C/mm2 [1].

• TiZr and TiZrV thin film (1µm) deposited onto chemically polished coppersubstrates [2].

• An important δmaxdecrease from above 2 to<1.4 already occurs after2h at 200°C (TiZr) and160°C (TiZrV), i.e. belowthe activationtemperature [2].

• δmax ~ 1.1 after 2h at250°C (TiZr) and 200°C(TiZrV) [2].

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 500 1000 1500 2000 2500 3000PE energy (eV)

SE

Y

A. r.

2 h 120 °C 2 h 160°C 2 h 200 °C 2 h 250 °C 2 h 300 °C

120°C x 2h

160°C x 2h

200°C x 2h

250°C x 2h

300°C x 2h

Courtesy of C. Scheuerlein

TiZrV sample

Surface coatings have been applied to many vacuum systems


ConclusionsNumerous processes exist by which the beam and the residualgas interact. The walls and surface characteristics of the vacuumsystem have a vital influence.

In addition to static and dynamic out-gassing properties, alsogeneration of electrons: photo- and secondary electrons areimportant

Electron cloud effect with its consequences on beam dynamicshas become a performance limiting effect in many accelerators

Future vacuum system designs must put emphasis on surfaceproperties of vacuum chambers and incorporate remedies for e-cloud effects to enable very high bunch currents and short bunchspacing


Literature

CAS Vacuum Technology, CERN99-05, 19 August 1999

G. Guignard, Selection of formulae concerning proton storage rings, CERN 77-10, 6 June 1977

W. Chao, M. Tigner, Handbook of Accelerator Physics and Engineering, World Scientific1999

J. D. Jackson, Classical Electrodynamics, John Wiley & Sons, 1975

H. Wiedemann, Particle Accelerator Physics, Springer-Verlag, 1993

P. J. Bryant, K. Johnsen, The Principles of Circular Accelerators and Storage Rings, Cambridge University Press

Y. Baconnier, G. Brianti, The stability of ions in bunched beam machines, CERN/SPS/80-2, 1980

E. Keil, B. Zotter, Landau damping of coupled electron-proton oscillations, CERN-ISR-TH/71-58, 1971

D. R. C. Kelly, Dust in Accelerator Vacuum Systems, PAC 97

C. Benvenuti, R. Calder, O. Gröbner, Vacuum for particle accelerators and storage rings, Vacuum 37, 8/9, 1987

O. Gröbner, Beam induced multipacting, PAC 97

beam vacuum interactions ii - cern

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