ess-bilbao initiative workshop. low energy transport and space-charge compensation schemes

Low EnergyTransport

and SpaceCharge

R. Duperrier

Front End

Ion sourceTheory

More electrodes

Codes

LEBTElectrostatic

Solenoids

sc neutralisation

Codes

RFQBasics

Beam dynamics

Current limits

Codes

Conclusions

Low Energy Transport and Space ChargeCompensation Schemes

Romuald Duperrier

Laboratoire d’Étude et de Développement pour les AccélérateursCEA/IRFU/SACM

Low Energy Transport and Space Charge March 17, 2009- Bilbao workshop 1 / 47

Low EnergyTransport

and SpaceCharge

R. Duperrier

Front End

Ion sourceTheory

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LEBTElectrostatic

Solenoids

sc neutralisation

Codes

RFQBasics

Beam dynamics

Current limits

Codes

Conclusions

Outline

1 Main parts of a Front End

2 The ion source extraction system

3 The LEBT line

4 The RFQs

5 Conclusions


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LEBTElectrostatic

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Conclusions

Outline



3 The LEBT line

4 The RFQs

5 Conclusions


Low EnergyTransport

and SpaceCharge

R. Duperrier

Front End

Ion sourceTheory

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LEBTElectrostatic

Solenoids

sc neutralisation

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RFQBasics

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Conclusions

Typical scheme for the front end

For a H+ front end, ECRIS are now the preferredsolution and allow to reach a few 10s to more than100 mA with a good emittance (< 0.2πµrad).A LEBT line is used to match the beam into the RFQ.It can also be used to pulse the beam with a slowchopper (r. t. of ∼ 100 ns) instead of pulsing thesource (r. t. of ∼ 2 ms). Monitoring diagnostics aresometimes inserted (CCD cams, DCCT).The RFQ creates the bunch structure etpre-accelerates the beam up to a few MeV.


Low EnergyTransport

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LEBTElectrostatic

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RFQBasics

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Conclusions

Outline



3 The LEBT line

4 The RFQs

5 Conclusions


Low EnergyTransport

and SpaceCharge

R. Duperrier

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Conclusions

Theoretical basics

[Langmuir & Blodgett, Phys. Rev. 24]

[Schneider et al, PAC’07]

Let us consider first a diodesystem extractor.To model the flow of ions inthe system, L. & B. proposedto solve the Poissonequation in a system ofdelimited by concentricspheres. For obviouspratical reasons, thesolution is reduced to afinite solid angle.The limit current is then:

I = 8πε09

(2qm

)1/2∆V 3/2 1−cosθ

−α2

with α a series of thefunction log(rb/ra).


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The current dependancy

It turns out that the geometry is linked to thecurrent and the ratio q/m for a given voltage.To illustrate, for heavy ions, it has been proposed toadjust the gap with a moveable electrode.The minimum of the divergence is then a strongfunction of q/m or I. This has to be integrated forthe current ramp up during the commissioning.

[Zaim & Alton, PAC’01]


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Conclusions

A hollow beam

Integrating spherical aberrations in the motionequation leads to solve D.E. like:

d2rdt2 = q

m

[G(z)r + G3(z)r3 + ...

]It turns out that extreme particles are more focusedand that a particular radius is more populated.Considering non linearities in the LEBT line, this pointis more advantage than a drawback.

[Batygin et al, PAC’95]Low Energy Transport and Space Charge March 17, 2009- Bilbao workshop 8 / 47

Low EnergyTransport

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Conclusions

A electron barrier electrode

[Sherman, PAC’07]

In diode system, LEBT electrons tend to go back upto the plasma electrode and may induce sparksand then voltage breakdowns.This effect can be suppressed by adding oneelectrode which is negatively polarized and asecond one at the ground to create a barrier.


Low EnergyTransport

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A fifth electrode?

[Delferrière et al, Rev. Sci. Instr. 79]

In case of nonmoveableelectrodes, it isalso to tune theextraction with afifth intermediateelectrode.This could helpfor tuning severalcurrents or otherchangingconditions.


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Conclusions

Benchmark with experiments(adjustment of unknown parameters)

In order to adjust parameters like the initial iontemperature in the simulation, benchmarks withexperiences are performed with a certain degreeof success...

[Delferrière et al, Rev. Sci. Instr. 75]


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Conclusions

Optimisation with PIC codes

Several commercial codes (2D, 2.5D or 3D) can beused for extraction system optimisation: PBGUN,IGUN, AXCEL, SCALA (see below), KOBRA.


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Conclusions

Outline



3 The LEBT line

4 The RFQs

5 Conclusions


Low EnergyTransport

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Conclusions

LEBT line based on electrostatic lenses

LEBT lines based on electrostatic einzel lensespermit very compact systems which can becombined with the source extraction.By splitting the lenses and playing with the differentpolarization, it is possible to provide beam steeringand fast chopping.

[Reijonen et al, LINAC’00]

Such system operatesat SNS for a H− peakcurrent of 35 mA.To compensate theeffect of the electronextractor (dipole), thesource is tilted withrespect to the LEBTaxis.


Low EnergyTransport

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Conclusions

Limits

[Han & Stockli, PAC’07]

For such currents, the beam size is very closed tothe lenses apertures, this induces emittancegrowths due to the high order terms and beamlosses (sparks).If the current is greater than 100 mA, there is aconsensus that this scheme is not suitable.For the SNS power upgrade, the peak current hasto be increased up to 59 mA. It is planned to use amagnetic focusing system (better acceptance, ...).


Low EnergyTransport

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Conclusions

Solenoids and space charge

The effects of S. C. and solenoid aberrations on thebeam have been investigated theoretically andexperimentally by Loschialpo et al in 1984.Due to the combined action of the nonlinear lensand the S.C., the initially uniform density becomeshollow or peaked (depending on distance).

[Loschialpo et al, J. Appl. of Phys. 57]

To cure this effect,long lenses [Bailey,EPAC’98] orcompact line toget a small beamsize are usualtechniques.


Low EnergyTransport

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Conclusions

A plasma lens

If we integrate the residual gas presence (ex.: H2) in thevacuum chamber, we can get the production of pairselectrons / ions (H+

2 ) via the ionization process:

p+H2→ p+e−+H+2

we assume that χ=Nbeam/ Ngas�1 with Nbeam thebeam density.


Low EnergyTransport

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Conclusions

Illustration

Example for a uniform beam of 100 mA @ 100 keV

0

2000

4000

6000

8000

10000

12000

14000

0 0.02 0.04 0.06 0.08 0.1

r(m )

E(V/m)

puits de potentiel

0

100

200

300

400

500

600

700

800

0 0.02 0.04 0.06 0.08 0.1

r(m)

V(v)

champ électrique

The e− are trapped in the beam and the ions H+2 are

repelled to the pipe. An electrical neutralization isobtained

⇒ space charge compensation


Low EnergyTransport

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Conclusions

Time scale

In a first approach, it can be estimated with theclassical formulation (DC beam):

τn = 1σNgasβc

with σ the ionization cross section, Ngas = P/kTroomand β the beam reduced speed.Evolution of neutralization degree, as a function oftime for a proton beam of 100 mA and 100 keV in adrift (1,5D PIC code computations):

Non lineartranscient phase:ion inertia, Te− .This rise time hasto be evaluatedfor pulsedoperation. [Ben Ismail et al, Phys. Rev STAB 10]


Low EnergyTransport

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Conclusions

The ion slowness

Proton beam of 100 mA and 100 keV in a drift forseveral pressures:

Non linear transcient due to the ion inertia isnon-existent at the beginning if P < 10−5 hPa.


Low EnergyTransport

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Conclusions

The solenoid combined with the spacecharge neutralisation

(H+ beam, 100 mA, 100 keV)

Ion density Electron density

Magnetic mirror at the edges.Transversal drift inside.


Low EnergyTransport

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Conclusions

Gas : nature and pressure (experiment)

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


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Conclusions

Electrical field comparison

(PIC code computation)

-80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80-12,50

-10,00

-7,50

-5,00

-2,50

0,00

2,50

5,00

7,50

10,00

12,50

Mass 100 @ 4e-4 hPa

Mass 100 @ 4e-5 hPa

Mass 4 @ 4e-4 hPa

Mass 4 @ 4e-5 hPa

R (mm)

Ex

(kV

/m)


Low EnergyTransport

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Conclusions

Emittance evolution

(PIC code computation)

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

1

1,2

1,4

1,6

1,8

2

2,2

2,4

2,6

2,8

3

Masse 100 @ 4e-4 hPaMasse 100 @ 4e-5 hPaMasse 4 @ 4e-4 hPa

Masse 4 @ 4e-5 hPa

z (m)

Gro

ssis

sem

ent

ém

itta

nce


Low EnergyTransport

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Conclusions

Gas : nature and pressure (conclusion)

Emittance enhancement with an increasing of thepairs production rate (pressure and/or crosssection).The enhancement with the heavy gas is due to across section which is multiplied by a factor 5 and agreater mass.


Low EnergyTransport

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Conclusions

The recombination

Above, the transmission of 2 m LEBT line with10−5 hPa of H2 and 4.10−5 hPa of Kr.The choice is then a compromise between loss inthe LEBT, loss in the RFQ and the rise time.


Low EnergyTransport

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Conclusions

The electron repeller

Let’s consider a dualsolenoid LEBT.A computation of thes. c. potential withthe correct boundaryconditions leads tothis steady state.For beam tuning, aDCCT is located atthe RFQ entranceand it may beperturbed by aelectron flow.A cleaning electrodemay help too forbeam tuning.


Low EnergyTransport

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Conclusions

Codes

The WARP code developed at Berkeley can beused to simulate the sc neutralisation in a LEBT. Thiscode is also used for e-clouds modeling.The SOLMAXP code developed at Saclay which isbased on a classical algorithm for modeling ofplasma coupled with a Maxwell solver permits suchsimulations too.


Low EnergyTransport

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Conclusions

Outline



3 The LEBT line

4 The RFQs

5 Conclusions


Low EnergyTransport

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RFQBasics

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Conclusions

A bit of history

In the early days, the injection of ions wasperformed with high voltage systems whichtypically produced continuous beam of ∼ 700 keV.

The bunch structure wasmade with one or severalbunchers. The efficiencywas between 60 to 70 %(Beijing proton linac).


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The principle

RFQ was invented by Kapchinsky from ITEP in thelate 60s. Teplyakov of the same instituteconstructed a first cavity.Important contributions to the RFQ have also beenmade by the LANL (POP in 1980). Since then, thisstructure has become very popular.

The features of the RFQ are that it bunches,focuses and accelerates charged particles byusing RF fields only.


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Conclusions

The cavity

A TE210 mode is used.The equivalent circuitof a 4 vanes RFQ.Typical view of a 4vanes RFQ (TRASCO).For a better stability,quadrants may becoupled (more RFpower cons.).For heavy ionsmachine, lowfrequencies arerequired (a few 10s ofMHz), inductancebased on stems arepreferred (Tokyo RFQ).


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Conclusions

4 subsections

1 At the RFQ entrance, a short section which rampsthe field amplitude performs the transition static totime focusing.

2 A delicate section called “gentle buncher”bunches adiabatically the beam.

3 Once the bunch is made, it is accelerated bydecreasing the synchronous phase and rampingthe modulation factor. Sometimes, the voltage isalso increased.

4 To help the matching in the MEBT line, the length ofthe last part of the cavity (“Fringe Field Section”)can be adjusted.


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The potential

A general solution of theLaplace equation whichobeys to the RFQsymmetries is detailed byWeiss in CAS proceedings[CAS 95-06].

This solution contains all the harmonics in infiniteseries but only a few harmonics are necessary towell describe a real RFQ. To facilitate the analysis,we shall consider a two terms potential:

U(r ,θ ,z) = V2

[A01r2cos2θ + A10I0(kr)cos(kz)

]with k = 2π/βλ


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The transverse focusing

By linearizing the transverse field componentsderived from the previous potential (smallamplitude), the equation of motion can besimplified to the following form:

d2xdτ2 + [Bsin2πτ + ∆rf ]x = 0

with 2πτ = ωt + φ and :

B = λ 2qVmc2R2

0and ∆rf = qπ2|sinφs |A10V

2mc2β 2s

At first order, the solution of this Mathieu equationis:

x(τ) = C0ejσt τ (1 + Csin2πτ)

with:σ2

t ∼B2

8π2 + ∆rf and C ∼ B4π2


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The longitudinal focusing

With the same technique (linearization for smallamplitude), Weiss show in the same reference thatthe second order equation of the evolution of∆φ = φ −φs can be written:

ddτ

(β 2

sddτ

∆φ

)+ π2qA10V |sinφs |

mc2 ∆φ = 0

Solving this oscillator D.E., one finds that the phaseadvance per period is:

σl(τ) =[

π2qA10V |sinφs |mc2β 2

s

]1/2

Let us note that:σl(τ) ∝ β

−1s


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Acceptances

In the same reference, it is given the expression ofthe hamiltonian for large amplitude oscillationsfrom which it is extracted the limit of the separatrix:

∆Wmax =±√

mc2β 2s qA10V (φscosφs− sinφs) ∝ βs

It has to be noticed that adding the space chargecontribution will lead to a smaller acceptance butalso provide a smaller emittance!For the transverse plane, the mean beam size isgiven by:

Rbeam =√

εt ,gβsλ

σt

Replacing by the expression for σt and settingRbeam = R0, one finds for a pure RF quadrupole(A10 = 0):

εt ,n = λqVmc2 6= f (R0)


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Space charge field

The space charge field for a uniformly chargeellipsoidal bunch can be calculated analytically[Lapostolle, CERN Report SG 65-15, 1965]:

Esx = 3Iλ(1−f )4πε0c(rx+ry )rz

xrx

Esy = 3Iλ(1−f )4πε0c(rx+ry )rz

yry

Esz = 3Iλ f4πε0crx ry

zrz

with f(p) for p<1 and f(1/p)when p>1 and p = γrz/rx ry


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Transverse current limit

Once these new field components are included inthe motion equation, it can be find that the newtransverse phase advance per focusing period is:

σt =

[q2λ 4V 2

m2c2R40 8π2 −

π2qA10V |sinφs |2mc2β 2

s− 3qIλ 3(1−f )

4πε0mc3(rx+ry )rx rz

]1/2

Solving for σt = 0, one finds:

It =

[qλV 2

mc2R40 8π2 −

π2qA10V |sinφs |2β 2

s λ 3

]4πε0c(rx+ry )rx rz

3(1−f )

See Wangler’s book for a more detailed analysis(Wiley series).


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Longitudinal current limit

The same approach allows to find the longitudinalcurrent limit expression:

Il =8π3ε0cA10V |sinφs |rx ry rz

3β 2s λ 3f

If we use the approximation for f = 1/3p, assumethat:

rz ∼ 3|φs|βλ/4π

and maximize the transverse beam size rx/y ∼ R0,one can find:

Il = 3πε0cA10V |sinφs |φ2s R0

2λ

Usually, the longitudinal current limit is lower thanthe transverse one. This induces that thebottleneck in a RFQ uses to be in the longitudinalplane. But this bottleneck does not always occurat the end of the gentle buncher.


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Current Limit for several RFQsTo illustrate thispoint, here agraph whichshows thelongitudinalcurrent limitnormalized bythe designpeak currentfor severalRFQs.

RFQs with a constant voltage give a minimum for Ilat the end of the acceleration section.The reduction of the product A10V |sinφs|φ2

s is notsufficiently damped by increasing the modulationfactor when the voltage is kept constant.


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Safety factors for several RFQs

Below, a report of these minimums (values beforethe gentle buncher end are ignored).

It has to be emphasized that the current limit is notthe only figure of merit in a RFQ (RF power, length,cost, ...) and the requirements for the beam losstolerance are a strong function of the duty cycle.


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Resonances

The space charge couples the three planes. Thiscoupling may induce emittance exchangebetween the planes if (simple approach):

σtσl

= pq with p and q ∈ N

This exchange could be seen from different pointsof views. This could lead to a undesirableemittance growth in a particular plane or, at theopposite, a way to define it.Personal opinion: this kind of game assumes thatyou know perfectly the transverse emittance thatyou inject in the RFQ and that the space chargecoupling is well predicted in the design phase→ dangerous game.


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RFQ codes

Several codes are available: PARMETQM-z/t(LANL), LIDOS (MRTI), RFQTRACK (Chalk River),TOUTATIS (CEA/Saclay) and RFQSIM (RAL).


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Outline



3 The LEBT line

4 The RFQs

5 Conclusions


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Conclusions

The main front end sections have their specifictechniques to manage the space charge:

ECRIS extraction system: geometry, voltage andnumber of electrodes,LEBT: plasma lens, length and aperture lens andcleaning electrode,RFQ: injection β , phase law, voltage law, ...

It has to be emphasized that a few parameters fordifferent sections couple these sections: boundaryconditions of the LEBT line, the β (recombination,longitudinal emittance, pressure, neutralisation risetime).


Low EnergyTransport

and SpaceCharge

R. Duperrier

Front End

Ion sourceTheory

More electrodes

Codes

LEBTElectrostatic

Solenoids

sc neutralisation

Codes

RFQBasics

Beam dynamics

Current limits

Codes

Conclusions

Many thanks to ...

Olivier Delferrière , Nicolas Chauvin

for their help!


ess-bilbao initiative workshop. low energy transport and space-charge compensation schemes

Technology