1. Laser Accelerators: The Technology of the Future (They Always Have Been and They Always Will Be ?) Cockcroft Institute Laser Lectures April 2008 Graeme Hirst STFC Central Laser Facility

2. Lecture 6 Plan Context Plasmas and acceleration Early results Dream beams Prospects Summary HHG (from lecture 4)

3. HHG can be understood using the 3-step model: tunnel ionisation, classical acceleration and recollision High Harmonic Generation An electrons return energy (the t=0 trajectory slope) is set by the time at which it tunnelled out. High energies appear only in a narrow time window High energy electrons generate attosecond X-rays. Once again a train of short pulses in time maps to a comb in frequency

4. High Harmonics - Spectrum The spectrum consists of odd harmonics whose energy falls rapidly to a broad plateau with a sharp cutoff Each plateau harmonic can have ~10 -6 of the drive energy Plateau Cutoff I p +3U p Conversion efficiency is affected by target ionisation, absorption and phase matching. The spectrum can be tailored by control of the driving E-field and quasi phase matching in a target capillary E-field control can also fine tune the harmonic wavelengths to fill spectral gaps above ~40eV. Reasonably efficient pulse-length preserving monochromators based on sagittal grating designs are now becoming available

5. High Harmonics - Prospects AVERAGE POWER: 10 -6 conversion of a 10mJ laser pulse should already give 10 9 h /pulse at 50eV which exceeds the pulse performance of undulators by a factor of ~10 4. Kilowatt class lasers should deliver >10 14 h /s which is 1-2 orders of magnitude below the average power from undulators. PHOTON ENERGY: Raising the cutoff energy will involve raising the electron energy. Options include using ions (higher I p ) or longer drive wavelengths (higher U p, but with more time for core wavepacket expansion hence lower recollision probability) SURFACE HARMONICS: Laser scattering from a rapidly oscillating dense plasma delivers keV harmonics with higher conversion efficiency than HHG in gases but requires a national scale drive laser

6. Laser Acceleration - References Phys Rev Letts, 43 (4) 267 Nature, 431 (7008) Phil Trans R Soc A, 364 (1840) Nature Phys, 2 (10) 696

7. Motivation Conventional accelerators are large and expensive (and this is not only true of world class particle physics machines) ~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

8. Laser Generated Fields The peak field in an EM wave is: E B P But the field is transverse and oscillating at >10 14 Hz so electrons acquire only keV energies (hence HHG cutoff) The field can be converted to a quasi-static (for co-propagating electrons) longitudinal one using plasma waves. Breakdown is not an issue as plasmas are already ionised.

9. Plasma Waves Basic plasma theory predicts electron density oscillations with which is ~40 times lower than optical frequencies if the electron density, n e, is 10 18 cm -3 However laser accelerators operate in an extreme regime where basic theory can break down. Complications include: Electrons becoming relativistic Plasma and optical behaviour becoming nonlinear Fields approaching the wave-breaking limit Analytic modelling now becomes difficult and large scale computational approaches (e.g. PIC) become important

10. Laser-Plasma Coupling Several mechanisms for coupling laser energy into plasma waves have been tried. They include: BEAT WAVE (PBWA) Two long pulses from lasers whose frequencies differ by p co-propagate through the plasma. The electrons respond to the field envelope. WAKE FIELD (LWFA) A single short pulse drives electrons forwards and sideways leaving a depleted volume in its immediate wake. In the so-called bubble regime electron re-injection can be restricted to a narrow phase window leading to monoenergetic output.

11. Acceleration Limits DEPHASING: Highly relativistic electrons travel faster than the plasma wave and eventually leave the high field region The velocity difference can be reduced by lowering n e, giving a longer dephasing length but also lowering E wb. It turns out: An energy gain of ~1GeV needs a dephasing length of >30mm DEFOCUSING: A lab-scale 10 19 W/cm 2 laser has a Rayleigh range 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

12. Early Results The highest energy electrons are rapidly accelerated in a small part of the wake, so their emittance is low. However their number is also low and varies widely from shot to shot. Laser pulses longer than the plasma period can be temporally subdivided by self modulation. The sub-pulses drive wakes which accelerate electrons to high energies in a few mm. But all oscillation phases are populated so the spectrum is broad. 025020015010050 Electron energy (MeV) 10 11 10 1 0 10 9 10 8 10 7 10 6 Number of electrons (/MeV/sr)

13. Low E/E – Dream Beam Early in this decade ~100MeV beams with few percent E/E were produced in three laboratories. Bunch charges could be tens or hundreds of pC and beam divergences just a few mrad. The secret was precise tuning of laser and plasma parameters to generate a strong wake, to self-inject over a very narrow phase range and to extract the beam before degradation. Energies were still limited by laser defocusing. Parameter windows were tight enough for shot-to-shot reproducibility still to be poor. But the principles were proven. n e = 6×10 18 cm -3 (upper), 2×10 19 cm -3 (lower)

14. 1 GeV Guiding of the drive laser beam using another laser had been reported in one of the dream beam papers A pulsed electric capillary discharge now created a radial density gradient in the target gas. The resulting light guide confined the 40TW laser beam for 33mm E=1.0±0.06 GeV, E=2.5% rms =1.6mrad, Q=30pC

15. 1 GeV Guiding of the drive laser beam using another laser had been reported in one of the dream beam papers A pulsed electric capillary discharge now created a radial density gradient in the target gas. The resulting light guide confined the 40TW laser beam for 33mm With 12TW drive and a narrower capillary, 50pC beams at 0.46±0.05GeV with E=6% were produced on every shot where the discharge-to-laser delay was correct A 0.9J laser pulse had produced a 25mJ electron bunch i.e. 3% energy conversion efficiency

16. Prospects STABILITY: Controlling self-injection is critical. It is very sensitive to experimental conditions, but reliably so. Current jitters are E ~5-10% and Q >10%. E/E is 2-5%. In addition to better experimental control, new approaches are being considered. EXTERNAL INJECTION: May be another route for controlling the beam. Electrons may be prepared using a second laser for PBWA. Alignment, synchronisation, emittance requirements are demanding. But they may need to be solved in any case for: STAGING: Controlling dephasing by further reducing n e will eventually become unmanageable (if only because of drive laser depletion). As with conventional accelerators the solution will be to use a larger number of discrete modules with the beam re-phased between them

17. Average Current - An Issue For some applications it hard to imagine plasma accelerators ever generating sufficient average power The 4GLS Energy Recovery Linac was specified at 0.6GeV/100mA (60MW power). The ILC beams are 45MW With 6% conversion a 1kW drive laser might deliver 0.6GeV/100nA (60W power) Few hundred MW turbines Few hundred watt alternator

18. Prediction Courtesy of Simon Hooker: It seems likely that in the next few years we will see very 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

19. LWFA Undulator Radiation Hot off the press (Nature Phys, 4 (2) 130) Note good fits between measured spectra and predictions based on the assumption of undulator radiation

20. 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 undulator radiation has been reported

21. Thank you !