review of beam dynamics issues in mw class ion linacs · black body radiation [chou, director’s...

Review ofBeam

DynamicsIssues in MW

Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics

Single particledynamics

Multiparticledynamics

Observedissues

Conclusions

Review of Beam Dynamics Issues in MW ClassIon Linacs

Romuald Duperrier

CEA/Saclay

IPAC 2010 - Kyoto

Review of Beam Dynamics Issues in MW Class Ion Linacs 1 / 42

Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Outline

1 MW Ion Linacs

2 Beam Physics

3 Single Particle Simulations

4 Multiparticle Simulations

5 Observed Issues

6 Conclusions


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Outline

1 MW Ion Linacs

2 Beam Physics



5 Observed Issues

6 Conclusions


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Applications of MW class ion linacs

Particle physics

Muons collidersNeutrinos factories

Condensed Matter

Neutron probeBiology, Magnetism, Polymers

Transmutationof long-lived radioactive wastes

Nuclear physicsBeams of short-lived elements

Super heavy elements

Technical Irradiation ToolTests of material (fusion, ...)


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Beam loss in MW class ion linacs

All these applicationsaim to use so highflux of secondaryparticles that thepower of the primaryion beam must reachone or several MW.Because aacceptable hands onmaintenance wouldmean beam loss of afew W/m, The loosedfraction has to bekept below 10−4

down to 10−7.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Layouts for MW class ion linacs

10-100 keV

LEBTIS RFQ MEBT NC DTL

NC/SC HWR

NC/SC QWR

NC CCDTL

NC PIMS

SC Spokes

NC CCL

SC Elliptical HEBT

2-5 MeV

120-180 MeV

1-8 GeV

f0

2-4 x f0


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Outline

1 MW Ion Linacs

2 Beam Physics



5 Observed Issues

6 Conclusions


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Space charge or self fields

This new generation of accelerators requires peakcurrent in the range of a few mA up to a one hundred ofmA.For this class of current, the beam as a source term inMaxwell equations can’t be neglected anymore:

∂t−→B =−

−→∇ ×−→E

−→∇ ·−→E = ρ/ε0−→

∇ ×−→B = µ0

−→J + ∂t

−→E /c2 −→

∇ ·−→B = 0

If the electric part is vanished by adding charge withopposite polarity, the magnetic field would remain.This is the reason why “self fields” is more appropriatethan “space charge”, but both expressions will be usedin this talk.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

The space charge neutralization

(100 mA proton beam, 100 keV)

Potentialwell

Electricfield

Considering a residual gas (ex.: H2) in the vacuumchamber, pairs of e− and ions (H+

2 ) will be produced byionization:

p + H2→ p + e−+ H+2

It is assumed that the beam density� gas density.This neutralization is mandatory for peak current higherthan 50 mA when electrostatic system are limited.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

The rise time

In a first and good approximation, the rise time for a DCbeam can be computed with the following classicalexpression:

τn = 1σNgasβc

with σ is the ionization cross section, Ngas = P/kTroomand β the reduced beam velocity (to be compared topulse length).If we plot the neutralizing charge provided in a drift by aDC and an AC beam (T/6) during one period T :

T

DC beam

T

AC beam

5/6 T

After one period, the same number of neutralizingcharge has been provided to the system.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Neutralization level for bunched beam

Because the beam bunch density is greater than theneutralizing particle density, the neutralization can’texceed the ratio bunch length / distance betweenbunches (βλ ).

[A. Ben Ismail, PhD thesis, 2005]


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Simulation with a PIC code: impact of a solenoid

(H+, 100 mA, 100 keV case)

H+2 electrons

Magnetic mirror at the edges.Transverse drift inside.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Emittance enhancement

[Gobin et al, Rev. Sci. Instr.,99]

Emittance enhancement with an increasing of the pairsproduction rate (pressure and/or cross section).The enhancement with the heavy gas is due to a crosssection which is multiplied by a factor 5 and a greatermass.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Gas stripping for H− and electron capture for H+

[Chou, Director’s review, Fermilab, 2005]

Energy dependence of total electron loss cross sectionfor H− incident on atoms.Transmission dependence for protons in 2 m LEBT.

Cross section decreases fastly with energy and the pressureis very low at high energy (SC): mainly a LEBT issue.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Magnetic stripping

When an H− moves in a magnetic field B, a force bendsits trajectory and tends to break it up since the protonsand electrons are bent in opposite directions.In the H− frame, E[MV/cm] = 3.197 p[GeV/c] B[T] wherep is the ion momentum in the lab.This phenomena will then be more important in the highenergy part of the machine. The effect is negligible iflow magnet field are used.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Black Body Radiation

[Chou, Director’s review, Fermilab, 2005]H− has two electrons, one tightly bound (13.6 eV),another loosely bound (0.75 eV).BBR is a newly discovered loss mechanism, dominantfor 8 GeV H−. For a multi MW beam, the loss rate is afew W/m.Cooling the vacuum pipe could solve the problem .

cross section

photon distribution

0.75 eV


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

The non linear nature of self fieldsLinear self fields correspond toan uniform density but thiscase is only valuable fortheoretical investigations.By essence, this non linearnature induces a spread of thetune.The consequence is that if thebeam doesn’t match with theisohamiltonian curves inphase space, an emittancegrowth will occur (a fewfocusing cells are necessaryto relax).

Isohamiltoniancurves

Beam

W'

W'

W'

W

W

W

W'

W'

W'

W

W

W

a) b)

Minimize the number of transitions in your linac!


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Instability for mismatched envelops

More than a filamentation,a mismatched beam can beunstable if the channelworking point is notproperly set.By linearization of the Xand Y envelop equationsfor small mismatched,Struckmeier and Reiserhave shown that the twomismatched modes (lowand high frequency) canexhibit an instability whenthe phase advance withoutspace charge per focusingperiod is greater than 90◦.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Periodic forces and parametric resonancesParticles in anaccelerator areoscillators driven by aperiodic force (Hill):

x ′′+ ω(s)x = 0When the two firstharmonics aredominant, Hill’s equationmay be reduced to theMathieu’s equation:d2xdτ2 + π2 [A + 2qsin(2πτ)]x = 0

Depending on q and A,the solution is stable orunstable. Stop-band canbe determined with theMathieu’s diagram.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Resonances with the radial fields in cavities

In Kapchinskiy’s book, itis shown how the radialfields couple thetransverse andlongitudinal planes.The transverse motionequation is reduced tothe Mathieu equation:A = 4 σ2

tσ2

land q = ∆ΦcotgΦs

When q ∼ 0, we haveresonance only forA = n2 or σt = n

2 σl .This is the reason whyσt > σl is preferred.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

PR with space charge (core-particle)

For a mismatched cylindricalbeam with uniform density, theparticle motion can be solvedby:

x ′′+ k2r (1 + δcos(krms))x = 0

with δ = 2M(1/η2−1).One can find out :A = 2η2/(1 + η2) and

q = 2M(1−η2)/(1 + η2)

Instabilities require highmismatch factors M and lowtune depressions, η . Butstable solutions maycorrespond to an amplificationof the amplitude.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

PR with space charge in 3D [Hofmann et al, EPAC’02 ]

To investigate the anisotropyeffects in ellipsoidal bunchesto go beyond this previoussimplified halo model, bystudying the stability ofsolutions of linearized Vlasovequation, it has been shownhow stop bands can arise inthe plane (η ,kz/kx ) fordifferent transv./long.emittances ratio.If working points are properlyselected in passband regions,equipartition is not necessary,this condition beinginaccessible for most of thepractical cases.

SPL

SNS

ESSReview of Beam Dynamics Issues in MW Class Ion Linacs 22 / 42

Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

High Order Modes [Jeon et al, NIM A 495 (2002)]

A beam passing througha cavity deposits afraction of its energy andcan excite modes.Numerical simulationindicates that cumula-tive transverse beambreakup instabilities arenot a concern for theSNS (mass).As little as ±0.1 MHzHOM frequency spreadstabilizes all theinstabilities from bothtransverse andlongitudinal HOMs.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

High Order Modes : still a difficult issue

Recent studies for the SPL mainly show that HOMs arenot a concern for this linac too (see Marcel Schuh’sposter THPE082).“Mainly” because machine lines may always correspondto a HOM.Recently, Tuckmantel shown that one order ofmagnitude for the current or the HOM frequency spreadis sufficient to induce an instability “from the noise”whatever the considered mode frequency [Tuckmantel ,BE-Note-2009-009 RF].For the decision about the necessity to equip the linacwith HOM dampers, a part of the answer is more a riskmanagement issue than a scientific issue.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Outline

1 MW Ion Linacs

2 Beam Physics



5 Observed Issues

6 Conclusions


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Frequency jumps

Different techniques tomanage frequencyjumps exist.They help to reduce theimpact of the frequencytransition on thebrilliance.Their drawback is areduced REG at thetransition.This reducedaccelerating efficiencybecomes negligiblewhen the output energyof the linac increases.

Frequency jump in an ion linac

R. Duperrier,1 N. Pichoff,2 and D. Uriot11CEA/Saclay, 91191 Gif sur Yvette cedex, France

2CEA/DAM Ile de France, BP 12-91680 Bruyeres-le-Chatel, France(Received 8 September 2006; published 1 August 2007)

Frequency jumps in an ion linac use to be made in order to provide a large transverse acceptance in thelow-energy part and a high accelerating gradient in the high-energy part. This frequency jump may inducea discontinuity in the average longitudinal force per focusing period and shrink the longitudinalacceptance of the linac if this transition is not performed carefully. In this paper, three techniques aredeveloped which produce a ‘‘certain’’ continuity of the channel at the transition between. The continuitytype is discussed. It is demonstrated that the longitudinal acceptance can be preserved whatever thefrequencies of the cavities in the linac. This point is very important when comparisons between differentcavity types are made (spoke and elliptical cavities for, instance). A few examples are shown to illustratethe performances of the three techniques.

DOI: 10.1103/PhysRevSTAB.10.084201 PACS numbers: 29.27.Bd, 29.27.Eg, 29.27.Fh, 41.75.�i

I. INTRODUCTION

Frequency jumps in ion linacs use to be made in order toprovide a large transverse acceptance (physical aperture) inthe low-energy part and a high accelerating gradient and/ora better shunt impedance in the high-energy part. Theminimization of the size of the cavities in the high-energysection is also interesting to reduce the cost because thesecavities are the most numerous in the accelerator. Smallercavities help to reduce the cryogenic load and induce acheaper fabrication. This frequency jump may induce adiscontinuity in the average longitudinal force per focusingperiod and shrink the longitudinal acceptance of the linac ifthis transition is not performed carefully. In Ref. [1], tech-niques are shown to manage the transition an radio fre-quency quadrupole operating at 350 MHz and a coupledcavity drift tube linac (CCDTL) operating at 700 MHz. It isexplained that as the frequency is doubled in the CCDTL, aconservative synchronous phase of �60 degrees is re-quired at the beginning of the structure to capture allparticles. The concept of the continuity of the phase ad-vance per unit length is discussed for the transverse planein order to provide a current and emittance independentdesign. This continuity simplifies significantly the match-ing at the transition. In this paper, we propose to developtechniques for designers to tune the phase and the field atfrequency transitions in an ion linac which include accep-tance and phase advance per unit length issues. During theEuropean Spallation Source studies in 2000 [2], we devel-oped a first technique to keep constant the confinementpotential shape at the frequency jump. The goal was tomaintain the beam in the achieved equilibrium state. Later,we proposed a different approach based on the continuityof the acceptance of the system. More recently, a thirdtechnique which is a mix of the first two has been proposed.

In this paper, these three techniques are developed andcompared to the classical method which is a matching atthe transition (tuning of the focusing elements to maintaina smooth evolution of the phase advance per meter in thefollowing section) keeping a high accelerating efficiency.

II. CONSTANT POTENTIAL SHAPE

The superconducting option for the European SpallationSource linac is made with different sections which operateat different frequencies (175, 350, and 700 MHz) [3]. Torender transparent these frequency jumps to the beam, afirst technique to keep the confinement potential shapeconstant at the transition has been developed [2]. Thistechnique aims at maintaining the beam in the achievedequilibrium state. This point is especially relevant when avery intense beam has to be transported [4]. As the longi-tudinal force is nonlinear (sine), assuming that the beamhas reached an equilibrium in the low frequency section, acontinuity of these nonlinearities is mandatory in order toavoid a new emittance growth in the high frequency sec-tion. From the equation of the longitudinal motion, it isshown in [5] that the potential well can be written:

V�� 2�

m��c�3frf

� qE0T

� �cos�s�sin�� sin�s � �cos�� 1��;

(1)

with �� the phase shift of the particle with respect to thesynchronous phase �s, frf the operating frequency, � thereduced speed, � the Lorentz factor, E0T the average fieldper focusing period taking into account the transit timefactor, c the speed of light,m the mass of the particle, and qits charge. Writing �� 2�frf�t and developing at third

PHYSICAL REVIEW SPECIAL TOPICS - ACCELERATORS AND BEAMS 10, 084201 (2007)

1098-4402=07=10(8)=084201(6) 084201-1 © 2007 The American Physical Society

[Duperrier, Pichoff & Uriot,PRSTAB 2007]


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Frequency jumps


f0 only

2 f0, constant Φs


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Frequency jumps


f0 only

2 f0, matched Φs


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Outline

1 MW Ion Linacs

2 Beam Physics



5 Observed Issues

6 Conclusions


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Start to end simulation

Once the referencedesign has been setup, it is necessary toevaluate thecollective effects inpresence of perfect orimperfect elements.To tend to “realistic”simulation, it isneeded to performstart-to-end transportfor estimating theimpact of haloproduced at lowenergy in the highenergy part. [Duperrier, EURISOL TM 2009]


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Track

Born in 2001 at Argone, this codehas been initially for the non lineartransport of several beams for RIA.Users: FERMILAB, SOREQ,ESS-B...

P.N. Ostroumov et al

Main featuresMost of theelements.Diagnostics.Distributed MC.Parallelized.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

TraceWin

Born in 1994 at Saclay, this code isable to simulate in a first order modeor in a PIC mode the beam motionin a linac.Users: LANL, J-PARC, LBNL,CERN, GANIL, IAP, INFN, RAL,...

D. Uriot et al

Main featuresMost of theelements.Diagnostics.Distributed MC.Part. parallelized.EPICS.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Outline

1 MW Ion Linacs

2 Beam Physics



5 Observed Issues

6 Conclusions


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

SNS feedback (1/2) [Zhang, EPAC 2008]

An important feedback from SNS is the confirmationthat HOM dampers wouldn’t be necessary for ms pulsemachines with peak current of 30 mA at 60 Hz with lessthan one hundred cavities.On the other hand, the operational gradient in the SCpart may vary widely from -100 % to +80%.Future errors studies for intense linacs will have toinclude a huge gradient spread in the cavity set.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

SNS feedback (2/2) [Zhang, HB 2008]

Unexpected longitudinal tails have been measured atthe entrance of the SC section.Is it the sign of the effect of the shrinkage of theacceptance at the frequency jump?Reduction of beam loss when the transverse phaseadvance is decreased would confirm this hypothesis.

SCL Acceptance, MEBT Particles and CCL ParticlesReview of Beam Dynamics Issues in MW Class Ion Linacs 33 / 42

Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

SNS feedback (2/2) [Zhang, HB 2008]

Unexpected longitudinal tails have been measured atthe entrance of the SC section.Is it the sign of the effect of the shrinkage of theacceptance at the frequency jump?Reduction of beam loss when the transverse phaseadvance is decreased would confirm this hypothesis.

Φs = -35◦(design: -20◦), sacrifices ∼100 MeV output energy


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

90◦ resonance stop band

To give rise to space charge induced resonances, a re-cent experiment has been carried out at GSI.Measurements of transverse phase space distributionsreveal a resonance stop band above zero current phaseadvance of 90◦ per focusing cell. These experimentalfindings agree very well with results from three differentbeam dynamics simulation codes.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Outline

1 MW Ion Linacs

2 Beam Physics



5 Observed Issues

6 Conclusions


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Conclusions

Beam dynamics in a high intense ion linac is a very richfield of physics.It requires skills in plasma physics as well as instatistical physics.Supported by activities of present and futureaccelerators, this domain progressed during the lastdecades and allows now very fine simulations based ona more mature knowledge of the beam behavior.Learning from SNS and on going studies, future MWlinacs with beam loss in the W range are within reach.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Neutralization stability for bunched beam

The beam space charge force for the neutralizingparticle acts as a periodic focusing channel in time.Baconnier shown that to get a stable motion for thisparticle, the bunch repetition frequency has to be:

fb >

√re ·c

2e ·mp· Ib

βR2

with mp is the proton mass in a.m.u., re the classicalradius of the electron, Ib the beam current and R itsradius [Baconnier, CERN-PS-PSR-84-24-REV-2].


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Design of the architecture based on singleparticle dynamics

Phase advances per focusing period for zero currentbeams must be below 90◦.Phase advance per meter (β ) must change adiabaticallyalong the linac despite of many lattice transitions(different types of focusing and inter-cryostat spaces).Choose working points to avoid parametric resonances(space charge and rf defocusing).Beam matching in the lattice transitions is veryimportant to avoid emittance growth and beam haloformation.Short focusing periods in the Front End to maximizeacceleration because σl < σt < 90◦ and σl ∼ E2Lp/β 3/2.To respect these rules, projection of transit time factorcan’t be used anymore. An optimization based onsingle particle transports is necessary. The optimummay be found with a space parameter discretization.


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Statistical analysis

With a large set of imperfect linacs, Cumulative DensityFunctions (CDF) can be established for any position.

But the discrete form of this CDF induces that theprobability to loose more than the more extremerecorded loss becomes null!


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Extreme Value Theory and Bootstrap technique

EVT provides a Generalized Extreme Value functionthat may represent the tail for extreme events:

Hξ σ µ (p) = exp

(−(

1 + ξp−µ

σ

)− 1ξ

)(1)

with µ, the location parameter, σ , the scale parameterand ξ a form parameter.To construct confidence intervals, one can resamplewith replacement from the actual data X to generate Bbootstrap samples X ∗.Properties expected from the replicate real sample areinferred from the bootstrap samples by analysing eachbootstrap sample exactly as we first analyzed the realdata sample. From the set of results of sample size B,we measure our inference uncertainties (variance).


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

GEV distribution

(EURISOL driver: proton case)

MEBT collimator

P(losses > 20 W) = 5%

HEBT dipole

P(losses > 10 W) = 3%


Review ofBeam


Class IonLinacs

R. Duperrier

MW ion linacs

Beam Physics



Observedissues

Conclusions

Confidence intervals at ±2σ

EURISOL driver: proton case(1000 resampled loss distributions for a fixed probability)

MEBT collimator HEBT dipole

CDF Lower Average Upperbound value bound

MEBT collimator 10% 8 W 11 W 14 WHEBT dipole 8% 0. W 1.15 W 2.82 W


review of beam dynamics issues in mw class ion linacs · black body radiation [chou, director’s...

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