Laser Accelerators: The Technologyof the Future

(They Always Have Been and They Always Will Be ?)

Cockcroft Institute Laser Lectures

April 2008

Graeme HirstSTFC Central Laser Facility

Lecture 6 Plan

• Context

• Plasmas and acceleration

• Early results

• “Dream beams”

• Prospects

• Summary

• HHG (from lecture 4)

HHG can be understoodusing the 3-step model:tunnel ionisation, classicalacceleration and recollision

High Harmonic Generation

An electron’s return energy (the t=0trajectory slope) is set by the time atwhich it tunnelled out. High energiesappear only in a narrow time window

High energy electrons generateattosecond X-rays. Once again atrain of short pulses in time mapsto a comb in frequency

High Harmonics - SpectrumThe spectrum consists of oddharmonics whose energy fallsrapidly to a broad plateauwith a sharp cutoff

Each plateau harmonic canhave ~10-6 of the drive energy

Plateau

CutoffIp+3Up

Conversion efficiency is affected by target ionisation, absorptionand phase matching. The spectrum can be tailored by control ofthe driving E-field and quasi phase matching in a target capillary

E-field control can also fine tune the harmonic wavelengths tofill spectral gaps above ~40eV. Reasonably efficientpulse-length preserving monochromators based onsagittal grating designs are nowbecoming available

High Harmonics - Prospects• AVERAGE POWER: 10-6 conversion of a 10mJ laser pulse

should already give 109 h/pulse at 50eV which exceeds thepulse performance of undulators by a factor of ~104. Kilowattclass lasers should deliver >1014 h/s which is 1-2 orders ofmagnitude below the average power from undulators.

• PHOTON ENERGY: Raising the cutoff energy will involveraising the electron energy. Options include using ions(higher Ip) or longer drive wavelengths (higher Up, but withmore time for core wavepacket expansion hence lowerrecollision probability)

• SURFACE HARMONICS: Laser scattering from a rapidlyoscillating dense plasma delivers keV harmonics with higherconversion efficiency than HHG in gases butrequires a “national scale”drive laser

Laser Acceleration - ReferencesPhys Rev Letts, 43 (4) 267

Nature, 431 (7008)

Phil Trans R Soc A,364 (1840)

Nature Phys,2 (10) 696

Motivation

Conventional acceleratorsare large and expensive(and this is not only trueof world class particlephysics machines)

~13km ~13km~4km

ILC (1TeV) cost $6.6bn, 22km of SCRF

The accelerating field is limited to~100 MV/m (often less)

FLASH (1GeV)cost €190M(not “green

field”), and has>50m of SCRF

Laser Generated FieldsThe peak field in an EM wave is: E

B

P

218

00

cmW 10I for TV/m 3

ZI2E

But the field is transverse and oscillatingat >1014 Hz so electrons acquire only keVenergies (hence HHG cutoff)

The field can be converted to a quasi-static (for co-propagatingelectrons) longitudinal one using plasma waves.

Breakdown is not an issue asplasmas are already ionised.

Plasma WavesBasic plasma theory predicts electron density oscillations with

0e2

ep men

which is ~40 times lower than optical frequencies if theelectron density, ne, is 1018 cm-3

However laser accelerators operate in an extreme regimewhere basic theory can break down. Complications include:

• Electrons becoming relativistic

• Plasma and optical behaviour becoming nonlinear

• Fields approaching the wave-breaking limit cemE pewb

Analytic modelling now becomes difficult and large scalecomputational approaches (e.g. PIC)become important

Laser-Plasma CouplingSeveral mechanisms for coupling laser energy into plasmawaves have been tried. They include:

BEAT WAVE (PBWA)

Two long pulses from lasers whose frequenciesdiffer by p co-propagate through the plasma.The electrons respond to the field envelope.

WAKE FIELD (LWFA)

A single short pulse drives electrons forwardsand sideways leaving a depleted volume in itsimmediate wake. In the so-called “bubbleregime” electron re-injection can be restrictedto a narrow phase window leading to“monoenergetic” output.

Acceleration LimitsDEPHASING: Highly relativistic electrons travel faster than theplasma wave and eventually leave the high field region

The velocity difference can be reduced by lowering ne, giving alonger dephasing length but also lowering Ewb. It turns out:

23e

e

n1length Dephasing

n1length dephasing a over gainEnergy

An energy gain of ~1GeV needs a dephasing length of >30mm

DEFOCUSING: A lab-scale 1019 W/cm2 laser has a Rayleighrange of a few mm. So ~1GeV needs beam confinement

This can be achieved in free plasma by filamentation or by“pre-drilling” with another laser

Or a capillary can be used

Early Results

The highest energyelectrons are rapidlyaccelerated in a smallpart of the wake, sotheir emittance is low.

However their numberis also low and varieswidely from shot to shot.

Laser pulses longer than the plasma period can be temporallysubdivided by self modulation. The sub-pulses drive wakeswhich accelerate electrons to high energies in a few mm. Butall oscillation phases are populated so the spectrum is broad.

0 25020015010050Electron energy (MeV)

1011

1010

109

108

107

106

Num

ber

of

ele

ctro

ns (

/MeV

/sr)

Low E/E – “Dream Beam”Early in this decade ~100MeV beams with few percent E/Ewere produced in three laboratories. Bunch charges could betens or hundreds of pC and beam divergences just a few mrad.

The secret was precise tuning of laser andplasma parameters to generate a strong wake,to self-inject over a very narrow phase rangeand to extract the beam before degradation.

Energies were still limited by laserdefocusing. Parameter windowswere tight enough for shot-to-shotreproducibility still to be poor. Butthe principles were proven.

ne = 6×1018 cm-3 (upper), 2×1019 cm-3 (lower)

1 GeVGuiding of the drive laser beam using another laser had beenreported in one of the “dream beam” papers

A pulsed electric capillary discharge nowcreated a radial density gradient in thetarget gas. The resulting light guideconfined the 40TW laser beam for 33mm

E=1.0±0.06 GeV, E=2.5% rms=1.6mrad, Q=30pC

1 GeVGuiding of the drive laser beam using another laser had beenreported in one of the “dream beam” papers

A pulsed electric capillary discharge nowcreated a radial density gradient in thetarget gas. The resulting light guideconfined the 40TW laser beam for 33mm

With 12TW drive and a narrowercapillary, 50pC beams at0.46±0.05GeV with E=6% wereproduced on every shot where thedischarge-to-laser delay was correct

A 0.9J laser pulse had produced a 25mJelectron bunch i.e. 3% energyconversion efficiency

ProspectsSTABILITY: Controlling self-injection is critical. It is very sensitiveto experimental conditions, but “reliably” so. Current jitters areE ~5-10% and Q >10%. E/E is 2-5%. In addition to betterexperimental control, new approaches are being considered.

“EXTERNAL” INJECTION: May be another route for controllingthe beam. Electrons may be prepared using a second laser forPBWA. Alignment, synchronisation, emittance requirementsare demanding. But they may need to be solved in any case for:

STAGING: Controlling dephasing by further reducing ne willeventually become unmanageable (if only because of drivelaser depletion). As with conventional accelerators the solutionwill be to use a larger number of discrete moduleswith the beam re-phased between them

Average Current - An IssueFor some applications it hard to imagine plasma acceleratorsever generating sufficient average power

The 4GLS Energy Recovery Linac was specified at0.6GeV/100mA (60MW power). The ILC beams are 45MW

With 6% conversion a 1kW drive laser might deliver0.6GeV/100nA (60W power)

Few hundredMW turbines

Few hundredwatt alternator

Prediction

Courtesy of Simon Hooker:

“It seems likely that in the next few years we will seevery compact laser-driven plasma accelerators with

• Controlled electron injection

• Energies up to a few GeV

• Energy spread <1%

• Pulse duration ~10fs

• Bunch charge 10-100pC

• Pulse repetition rate 10Hz”

LWFA Undulator RadiationHot off the press(Nature Phys, 4 (2) 130)

Note goodfits betweenmeasuredspectra andpredictionsbased on theassumptionof undulatorradiation

Summary• Over 25 years laser plasma accelerators became capable of

generating ~100MeV electrons with reasonable emittance. However their relative number was small and their parameters hard to reproduce

• In the last 5 years the advent of high power, short pulse lasers has delivered monoenergetic beams with low emittance and much higher bunch charge. As laser and plasma control improves, so shot-to-shot bunch variations decrease

• In the last few months the first use of plasma accelerated electrons to produce undulatorradiation has been reported

Thank you !