WO2016166549A1

WO2016166549A1 - Coherent radiation source

Info

Publication number: WO2016166549A1
Application number: PCT/GB2016/051058
Authority: WO
Inventors: Dino Anthony Jaroszynski; Bernhard ERSFELD; Mohammed Ranaul ISLAM
Original assignee: University Of Strathclyde
Priority date: 2015-04-15
Filing date: 2016-04-15
Publication date: 2016-10-20
Also published as: GB201506352D0

Abstract

A radiation source and an associated method of use. The radiation source includes a laser-plasma wakefield accelerator that is configured to pass at least one laser pulse through a plasma and inject a stream of plasma electrons into at least one bubble in a wake of evacuated plasma bubbles, wherein at least one electron bunch inside the bubble is modulated, and at least one modulated electron bunch is caused to radiate thereby to emit radiation.

Description

Coherent Radiation Source

Field of the Invention

The present invention relates to a method and apparatus for producing electromagnetic radiation using accelerated charged particles.

Background of the Invention

Free-electron lasers are brilliant sources of coherent X-rays that are powerful research tools for investigating the structure of matter. Free-electron lasers are very large devices that require huge investments and incur high running costs. Reducing the size of coherent X-ray sources would make them more affordable and widely available.

Coherent radiation from a free-electron laser is produced when a relativistic electron beam is bunched on a wavelength scale by the ponderomotive force of combined radiation and undulator fields. A self-amplification of spontaneous emission free- electron laser amplifies shot-noise radiation in an undulator through a collective instability that leads to exponential growth of the electron bunching and radiation intensity. The high brilliance, tuneability and short pulse duration of free-electron lasers makes them extremely versatile and useful tools for temporal and spatially resolved studies of atomic and molecular structure. However, because of the high cost of free- electron lasers, efforts are being made to develop alternative, compact radiation sources based on conventional lasers.

Progress is being made on realising radiation sources using high power lasers. These sources currently cover a wide range of photon energies from meV (far-infrared) to MeV (gamma rays), but their usefulness is limited by relatively low brightness and coherence. Laser-driven high-order harmonic generation in gas, on the other hand, is a promising compact ultra-short pulse coherent radiation source, but has limited efficiencies and spectral bandwidths. Radiation sources based on laser-plasma wakefield accelerators are also being explored. Laser-plasma wakefield accelerators exploit the high electric fields of laser- driven plasma wakes. They have been used to produce incoherent synchrotron and betatron X-ray radiation, and are being developed for use in compact free-electron lasers and ion channel lasers. Laser-plasma wakefield accelerators form charge density waves, with associated electrostatic fields, that trails an intense laser pulse propagating through plasma. These electric fields can be used to accelerate charged particles over very short distances with high accelerating gradients. Laser-plasma wake-field accelerators can generate particle beams with energies equal to those delivered by conventional machines some tens or hundreds of metres long. Laser driven plasma accelerators can power radiation sources, such as synchrotrons, to form compact sources of short pulses of charged particles and tunable radiation.

Undulators may be used to derive electromagnetic radiation from accelerated charged particle beams and thereby form a radiation source. Such undulators are based on arrays of permanent magnets arranged so that their magnetic fields periodically deflect a charged particle beam passing through them. The transverse motion thus imparted to the charged particle beam produces so-called undulator or wiggler synchrotron radiation, which forms the basis of modern synchrotron sources. Undulators can also be formed by counter-propagating laser beams that cause similar transverse motion, but with a very much shorter wavelength than a conventional undulator. The radiation process from a laser undulator is also known as Thomson scattering.

Summary of the Invention

According to the present invention, there is provided a radiation source comprising a laser-plasma wakefield accelerator that is configured to pass a laser pulse through a plasma and inject at least one stream of electrons into at least one bubble in a wake of evacuated plasma bubbles, wherein at least one electron bunch inside at least one bubble is modulated, and at least one modulated electron bunch is caused to radiate thereby to emit radiation.

The electron beam may be modulated using a density modulation in the plasma or a velocity modulation in the plasma. The modulation may be a periodic modulation or may be an aperiodic modulation. For example, the modulation may be a periodic density modulation or a periodic velocity modulation with a short wavelength period of between 60 microns and Angstroms. Aperiodic modulation may consist of a quasi- periodic chirped modulation, where the periodicity decreases or increases monotonically.

Modulation of the plasma electrons to form a modulated electron bunch may occur before or after injection into the plasma bubble. The modulated electron bunch can result in the emission of brilliant femtosecond or shorter duration coherent soft X-ray radiation pulses having wavelengths shorter than 200 nm, for example in the 2 - 50 nm spectral range or shorter such as 1 Angstrom and below. This can be achieved using a simple and compact arrangement.

The laser-plasma wakefield accelerator may be set up to cause two streams of electrons to be simultaneously injected into at least one bubble, in such a way that they cross. This causes pre-bunching due to streaming instability, which results in electron modulation inside at least one plasma bubble. In this case, the laser-plasma wakefield accelerator may be set up to cause the modulated electrons to radiate inside at least one plasma bubble, thereby to cause emission of radiation within at least one bubble. This radiation is then emitted from at least one bubble. The radiation source may comprise a modulator for modulating the plasma density in the vicinity of the bubble or bubbles, so that the electrons injected into the bubble or bubbles are pre-modulated. By in the vicinity of the bubbles, it is meant close to or overlapping the bubbles. The laser-plasma wakefield accelerator may be set up to form a relativistic reflector at the back of the bubble for reflecting electron bunches. The relativistic reflector may be arranged to cause a Lorentz contraction of the modulated electron bunch. Betatron motion of the modulated electrons causes the emission of radiation within the bubble. This radiation is then emitted from the bubble.

The laser-plasma wakefield accelerator may be set up to allow the modulated electron beam to be emitted from the bubble. In this case, a radiator for causing the modulated electron beam to emit radiation is provided downstream of the bubble. Movement of the modulated electron beam through the radiator causes undulating motion of the modulated electrons, which in turn causes the emission of radiation.

According to another aspect of the invention, there is provided a method that uses a laser-plasma wakefield accelerator, the method comprising: passing a laser pulse through a plasma to generate a wake of evacuated plasma bubbles; injecting at least one stream of plasma electrons into at least one bubble in the wake of evacuated plasma bubbles; modulating at least one electron stream before or after injection into at least one plasma bubble to form a modulated electron bunch; and causing at least one modulated electron bunch to radiate, thereby to generate radiation. The method may further involve causing the laser-plasma wakefield accelerator to simultaneously inject two or more streams of electrons into a bubble, in such a way that they cross at the rear of the bubble, thereby to cause electron modulation inside the plasma bubble. In this case, the method may involve setting up the laser-plasma wakefield accelerator to cause the modulated electrons to radiate inside the plasma bubble, thereby to cause emission of radiation within the bubble. This radiation is then emitted from the bubble. Two or more streams of electrons may be injected into multiple bubbles. In this case, multiple beams of radiation may be emitted simultaneously. The method may involve using a modulator for modulating the plasma density in the vicinity of the bubbles, so that the plasma electrons injected into the bubble are pre- modulated.

The method may involve forming a relativistic reflector at the back of the bubble. The relativistic reflector may be arranged to cause a Lorentz contraction of the beam. Betatron motion of the modulated electrons causes the emission of radiation within the bubble. This radiation is then emitted from the bubble.

The method may involve allowing the injected, modulated electron beam to be emitted from the bubble. In this case, the method may further involve using a radiator outside the bubble for causing the modulated electron beam to emit radiation.

The method may further involve varying the wavelength of the radiation emitted by varying the plasma density or the depth of modulation.

Brief Description of the Drawings

Various aspects of the invention will now be described by way of example only with reference to the accompanying drawings, of which:

Figure 1 is a schematic view of a laser-plasma wakefield accelerator output; Figure 2(a) is a schematic view of a first scheme for generating radiation using a modulated electron beam;

Figure 2(b) is a schematic view of a variation of the first scheme of Figure 2(a);

Figure 3(a) is an image of a plasma bubble in which an injected electron bunch has been formed, from a simulation;

Figure 3(b) is an image of a modulation that has arisen from streaming instability;

Figure 3(c) shows a Fourier transform or spectrum of the bunching indicating the wavelength (8 nm) which is consistent with measurements;

Figure 3(d) shows trajectories of electrons as they undergo betatron motion inside the bubble;

Figure 4(a) shows typical VUV spectra at a first plasma density;

Figure 4(b) shows typical VUV spectra at a second plasma density;

Figure 4(c) shows typical VUV spectra at a third plasma density;

Figure 5 is a logarithmic plot of the measured photon energy versus plasma density for various experiments along with the simulated wavelengths for the corresponding densities;

Figure 6(a) is a schematic view of a second scheme for generating radiation using a modulated electron beam;

Figure 6(b) is a schematic view of a second scheme for generating radiation using a modulated electron beam, and

Figure 7 is a logarithmic plot of bunch spacing versus ripple amplitude for simulations where the depth of modulation has been varied. Detailed Description of the Drawings

A laser-plasma wakefield accelerator produces relativistic electron beams by passing a laser pulse through plasma and injecting groups of charged particles into the plasma density wake of the laser pulse so that the group is accelerated by the wake. The accelerating structure of the laser-plasma wakefield accelerator is a wake of evacuated plasma bubbles created by a combination of the laser ponderomotive force and the restoring force of background ions. In laser-plasma wakefield accelerators, electrons can be injected from an external source or from the plasma. The present invention is based on electron injection from the plasma itself. Plasma electrons acquire momentum from the laser pulse to form a narrow sheath around the evacuated plasma bubbles. Plasma electrons can be injected into the plasma bubble when their velocity exceeds that of the bubble. They enter the bubble with an initial transverse momentum. The injected electrons accelerate to high energies while undergoing transverse betatron oscillations, due to the bubble restoring forces, with a wavelength:

where λ_ρ is the plasma wavelength and γ is the Lorentz factor of the electrons. This gives rise to synchrotron-like betatron radiation.

The present invention is based on the realisation that modulation of the plasma electrons before or after injection into a bubble can be used to create a modulated electron bunch, which when allowed or caused to radiate produces coherent radiation of the same wavelength as the wavelength of the modulated electron bunch. This can be used to generate brilliant attosecond duration coherent soft X-ray radiation. In experiments based on streaming instability (as described in detail below) X-ray pulses have been generated in the 2 - 50 nm spectral range. Figure 1 is a basic schematic of a laser-plasma wakefield accelerator showing a plasma or gas jet and a laser beam. Interaction between the laser and the plasma occurs over a defined interaction region. The length and diameter of the interaction region depends on the plasma density. Lower density requires a larger volume interaction region. As an example, for a density of 10¹⁹ cm^"3, the interaction region has a diameter of 10 - 50 μηι and a length of 2 mm.

The short pulse laser beam is focussed so that it has an intensity at focus above that for relativistic self-focussing, which is greater than 10¹⁸ WcnT² for a 800 nm laser. In addition, the F-number of the focussing system is chosen to give a focal spot diameter slightly larger than the plasma wavelength, which for a density of 1.7* 10¹⁹ cm^"3 is 8 μΓΠ. Relativistic self-focussing further reduces the focal spot size to match the plasma wavelength. The pulse length is chosen to be approximately equal to the plasma wavelength. Modulation of the plasma electrons produces a modulated electron bunch. This is caused to radiate to create coherent radiation in the interaction region and inside or outside a plasma bubble that travels close to the speed close of light in vacuum.

Modulation of the injected electrons can be produced in a number of ways. For example, for modulation inside the bubble, two electron beams with different velocities could be generated such that they cross at the back of the bubble, thereby to cause a plasma streaming instability, which results in the formation of a modulated electron bunch. By electron bunch, it is meant a group of electrons that are at least a part of an electron stream or beam. Alternatively, for modulation outside the bubble, the plasma density can be modulated. This can be done in a number of ways. For example, a modulated plasma capillary could be used, or one or more secondary lasers could be used to produce a beat wave interference pattern that leaves behind a density modulation corresponding to the periodicity of the interference fringe. Equally, short-duration obliquely angled laser pulses could be used to generate a transverse force. This density modulation can be produced through the ponderomotive force or ionisation or a combination of the two. Another option for modulating the electron beam is to use a velocity modulation in the plasma. In any case, modulation of the electrons results in a modulated electron bunch. Figure 2(a) shows a schematic representation of a radiation source that uses a plasma streaming instability modulation. In this case, two electron beams are injected from opposing sides of the bubble, so that they cross substantially at the injection point. Before injection, electrons are first accelerated by the ponderomotive force of the laser in the forward direction while simultaneously being ejected transversely until the restoring force of the plasma ions pulls them back. When the laser has passed electrons are slowed down and then accelerated backwards. They reach their maximum backward potential at a point close to the point where the sheath current bifurcates into two streams. Some electrons stream outwards. Others are attracted towards the ion bubble and begin to decelerate until they become stationary and accelerate to eventually reach the bubble velocity, at which point they are injected. In practice, only a short electron bunch is injected if close to the threshold for injection. The laser intensity is adjusted so that injection occurs close to threshold for injection. This is described in more detail below. Coherent X-ray emission occurs through a process of density modulation at injection and subsequent coherent betatron radiation. Periodic density modulation arises from a streaming instability that occurs when the injected electrons, or electrons about to be injected, cross at the rear of the bubble-shaped accelerating structure. This results in a modulated electron bunch. The bunch length is governed by charge build-up at the rear of the bubble, or a variation in the phase velocity of the bubble, which sets a time dependent threshold for injection. Inside the plasma bubble, a radiator is provided. By radiator, it is meant that the electric and magnetic field strength distribution in the bubble are such as to cause transverse or betatron motion of the modulated electron beam, thereby to cause emission of coherent radiation. Transverse betatron motion of the nanometre density modulated electron bunch through the radiator leads to emission of ultra-short duration pulses of coherent synchrotron or curvature radiation. The photon energy is observed to be proportional to the square of the plasma density, which enables tuneability and scalability providing a very useful and compact source of brilliant, attosecond duration, coherent soft X-ray photons. The relationship between the plasma density and photon energy will be discussed in more detail later.

Close to the threshold for injection electrons in the sheath-crossing region have relativistic longitudinal and transverse momenta, and cross at an angle with respect to the axis, which is defined by the centre of the bubble and its direction of propagation. The stream density in the sheath-crossing region is ^«4* 10²¹ cm^"3, for a background plasma density of ^«10¹⁹ cm^"3, which is more than twice the critical density, n_c~1.7x 10¹⁹ cm^"3 for a 800 nm laser beam. The overlap region where streams cross contains more than 10⁶ electrons (0.16 pC). The two streams have similar longitudinal momenta and equal and opposite transverse momenta. The bunch is highly chirped across the bunch (energy varies across the bunch) longitudinally and transversely. The streaming instability is a combination of two-stream and filamentation instabilities, which leads to very rapid growth of modulation. For the momentum chirp observed in simulations, the wavelength of the modulation is restricted to a range of which corresponds to a range of 15-39 nm. The measurements of emitted radiation compare well with the simulations, which show nearly 100% periodic modulation with a wavelength of around 15 nm.

Figure 2(b) shows a schematic representation of another radiation source based on plasma streaming instability modulation. As for the arrangement of Figure 2(a), two electron beams are injected into a bubble, so that they cross substantially at injection. Periodic density modulation arises from a streaming instability that occurs when the injected electrons or electrons about to be injected, cross at the rear of the bubble- shaped accelerating structure. This results in a modulated electron bunch. The modulated bunch length is governed by charge build-up at the rear of the bubble or a variation in the phase velocity of the bubble, which sets a time dependent threshold for injection. In this case, the modulated bunch is emitted from the bubble and subsequently transmitted through a radiator, which causes emission of coherent synchrotron radiation. The radiator may be of any suitable form, for example an electrostatic, magnetostatic, electromagnetic or plasma undulator. The electromagnetic radiator could also be a counter-propagating laser beam.

The modulation scheme of Figure 2(a) has been tested. In experiments, the laser- plasma wakefield accelerator was optimised to operate just above threshold for injection and soft X-ray and electron spectra were recorded simultaneously using electron and X-ray spectrometers to determine whether radiation emitted correlated with the formation of an electron beam.

Figure 3(a) shows an injected electron bunch after the beams have crossed showing the modulation (b) that has arisen from the streaming instability. Figure 3(c) shows the Fourier transform or spectrum of the bunching indicating the wavelength (8 nm) which is consistent with measurements. Figure 3(d) shows the trajectories of electrons undergoing betatron motion inside the bubble. The radiation source of Figure 2(a) has been tested experimentally. For these experiments, a 30 - 40 femtosecond duration, 20 - 30 terawatt, 800 nm laser pulse is focussed to a spot size of around 40 microns (1/e² in intensity) onto a 2 mm diameter helium gas jet with a density of 1-2* 10¹⁹ cm^"3, the laser-plasma wakefield accelerator was optimised by adjusting the focal position and found to have an optimum at about 1/3^rd of the (leading) ramp length, which is consistent with operating just above threshold for injection for the laser parameters. Both electron and soft X-ray spectra were then simultaneously recorded using spectrometers, situated approximately 2 m and 6 m, respectively, downstream from the gas jet. The X-ray spectrometer slit and beam pipe apertures defines a collecting angle of 1.2*10^"7 steradian. Figure 4(a) shows typical VUV spectra. Each spectrum of Figure 4(a) was taken under the same measurement conditions, but due to instability of the laser, variations in the intensity are evident. However, the peak positions are clustered around the same wavelength. From this, it can be seen that for a density of approximately 1.9* 10¹⁹ cm^"3 the spectra peak cluster around 8 nm. Figure 4(b) shows that for a density of 1.1 * 10¹⁹ cm^"3 the spectra peak between 20 - 30 nm. Figure 4(c) shows that for a density of 8.8* 10¹⁸ cm^"3 the spectra peak between 30 - 40 nm. In general a larger number of photons are emitted for lower measured charge, which indicates that the modulation is enhanced close to threshold for injection. The stability of the XUV pulses is 4.1 % for 8.74±0.36 nm peaks observed with an r.m.s. spectral width of 2.15±0.35 nm. For a Fourier transform limited pulse, this amounts to a 71.1 attosecond (FWHM) (30.2 attosecond r.m.s.), or 2-3 cycle pulse. For 39.9 ±1.3 nm (3.3% stability) at 8.8x 10¹⁸ cm^" ³ the mean r.m.s. spectral width is 5.7 nm. The wavelength stability depends on the shot-to-shot stability of the laser and reproducibility of the plasma. The electron energy varied between 180 MeV and 130 MeV between the lowest and highest densities used in the experiments. The charge close to threshold is 1-10 pC.

Figure 5 shows a logarithmic plot of photon energy versus plasma density. From this, it can be seen that the log plot has a slope of two, which means that there is a substantially quadratic relationship between the photon energy and plasma density. This means that varying the plasma density provides a controllable way of setting the photon energy and consequently the wavelength of the emitted radiation. Therefore, this provides a tunable radiation source.

Figure 6(a) is a schematic representation of another modulation scheme. In this case, the electron beam is modulated prior to injection into the plasma bubble to form at least one modulated electron bunch, and the laser-plasma wakefield accelerator operational conditions are selected to cause formation of a relativistic reflector at the edge of the plasma bubble, and a radiator within the plasma bubble. By relativistic reflector, it is meant that the conditions in the plasma are such that the incoming electron bunch, which is travelling at a speed close to the speed of light in vacuum, and in the opposite direction of travel to the bubble, is turned round and travels with the bubble. By radiator, it is meant that the electric and magnetic field strength distribution in the plasma bubble are such as to cause transverse or betatron motion of the modulated electron bunch, thereby to cause emission of coherent radiation. Pre-modulation of the electron beam to form a modulated electron bunch can be implemented by varying the density of the plasma or the velocity of the plasma. This can be done in a number of ways, for example by using a modulated plasma capillary or one or more secondary lasers for producing a beat wave interference pattern that leaves behind a density or velocity modulation corresponding to the periodicity of the interference fringe.

The relativistic reflector can be produced by periodically varying the phase velocity of the bubble (so called downramp injection) or varying the charge build-up and potential at the back of the laser-plasma wakefield accelerator. The potential must be just sufficient to reflect or inject the particle into the accelerating structure of the laser- plasma wakefield, i.e. it must be close to threshold. This allows the potential to act as a discriminator so that the periodic plasma bunching results in a train of short bunches.

The relativistic reflector compresses the modulated plasma electron bunch into a very short period modulated bunch. This process relies on relativity, which produces a double Doppler contraction of the wavelength. The contracted wavelength can be varied by adjusting the velocity of the relativistic reflector. This can be achieved by varying the density, modulation depth, or by using a density gradient. The relativistic contraction is given by:

and /3_φ = ν_φ l c , where ν_φ is the average velocity of the "reflector", which is very close to the speed of light in vacuum, c. The velocity can be controlled in a number of ways. To get to shorter wavelengths a higher phase velocity is required. The phase velocity, ν_φ , can also depend on the modulation depth of the plasma segment. Therefore, the phase velocity may be tuned as a function of periodicity of the modulation and its depth.

The radiator is formed by electrostatic forces of the laser-plasma wakefield accelerator bubble structure, where transverse betatron oscillations produce the transverse acceleration, which results in the emission of radiation. Because the transverse acceleration is very large, the betatron oscillations cause radiation to be emitted. Because of the modulation of the electron bunch, the radiation emitted is coherent. Hence, the system radiates effectively like a coherent synchrotron source. Because the energy of the electron bunch can be very high it produces coherent radiation at a wavelength that is ly^ times smaller than the modulation wavelength of the plasma before the relativistic reflector.

Figure 6(b) is a schematic representation of yet another modulation scheme. As for Figure 6(a), the electron beam is modulated prior to injection into the plasma bubble, and the laser-plasma wakefield accelerator operational conditions are selected to inject electrons into the plasma bubble. In addition, the laser-plasma wakefield accelerator operational conditions are selected to cause formation of a relativistic reflector at the rear of the plasma bubble, so that incoming modulated electron bunches, which are travelling in the opposite direction of travel to the bubble, are turned round and travel with the bubble. However, in this case, a radiator is provided outside the bubble. The radiator may be an electromagnetic, electrostatic, magnetic or plasma undulator. For example, the radiator could be an electromagnetic undulator or wiggler with a wavelength and undulator parameter that is matched to the electron modulation period (i.e. the emission wavelength of the undulator or wiggler is matched to the bunching wavelength) or to another laser-plasma wakefield accelerator where it undergoes betatron emission. Alternatively, the electromagnetic undulator could be formed using a counter-propagating laser beam. This would produce coherent Thomson scattering. Alternatively, the modulated electron beam could be injected into a second laser- plasma wakefield accelerator where the betatron motion causes radiation. Electrons leaving the bubble enter the radiator which results in coherent synchrotron radiation.

Figure 7 shows a logarithmic plot of bunch spacing versus ripple amplitude. In this context bunch spacing is the wavelength of the modulated electron bunch and the ripple amplitude is the amplitude of the modulation applied to create the modulated electron bunch. From this, it can be seen that the log plot has a linear slope, which means that there is a well-defined relationship between bunch spacing and ripple amplitude. Since the bunch spacing defines the wavelength of the emitted radiation, by varying the modulation amplitude, the wavelength of the emitted radiation can be varied and/or controlled. The coherent X-ray source of the invention is based on a high power laser with high peak powers. This can be relatively compact. In practice, the laser can fit on two optical benches and the coherent x-ray source can fit on a footprint of 4x8 m². The repetition rate can be up to 10 Hz with currently available lasers and with the next generation of high power lasers, based on diode-laser technology, could be increased up to 100 Hz or 1 kilohertz. The parameter range envisaged is 200 nm to 2 nm, with a 20-40 TW lasers, and down to 1 Angstrom or less with a 300-400 TW laser. The device has been experimentally demonstrated in the range of 2 - 50 nm using a 30 TW laser. The VUV or X-ray pulse length is less than 500 attoseconds, possibly less than 100 attoseconds, and could be as short as 1 - 5 attoseconds in the hard X-ray spectral region. The number of photons per pulse is around 10¹⁰ but could be increased by increasing the charge in the modulated region of the bunch. Conservatively, this gives a peak brilliance of >10³¹ photons/second/mm²/mrad²/0.1 % bandwidth, but could be as high as 10³³ photons/second/mm²/mrad²/0.1 % bandwidth if the X-ray pulse has a duration of 100 attoseconds as observed in simulations.

The present invention provides an ultra-compact method of producing few-cycle pulses of coherent soft X-ray radiation using a laser-plasma wakefield accelerator. Pulses have been generated with durations of 100 attoseconds and having 10¹⁰ photons, with peak brilliances in excess of 10³¹ photons/s/mrad²/mm²/0.1 %BW and in the 2-50 nm wavelength region, overlapping with the "water-window". The coherent radiation source of the invention is based on a simple idea requiring electrons to be bunched on a wavelength scale of the wavelength of the output radiation desired. A skilled person will appreciate that variations of the disclosed arrangements are possible without departing from the scope of the invention. Accordingly the above description of the specific embodiment is made by way of example only and not for the purposes of limitation. It will be clear to the skilled person that minor modifications may be made without significant changes to the operation described.

Claims

A radiation source comprising a laser-plasma wakefield accelerator that is configured to pass at least one laser pulse through a plasma and inject a stream of plasma electrons into at least one bubble in a wake of evacuated plasma bubbles, wherein at least one electron bunch inside the bubble is modulated, and at least one modulated electron bunch is caused to radiate thereby to emit radiation.

A radiation source as claimed in claim 1 wherein the laser-plasma wakefield accelerator is arranged to cause at least two streams of electrons to be simultaneously injected into a plasma bubble, in such a way that they cross, thereby resulting in electron modulation inside the plasma bubble and formation of the modulated electron bunch.

A radiation source as claimed in claim 2 wherein the laser-plasma wakefield accelerator is arranged to cause at least two streams of electrons to be injected into multiple plasma bubbles, in such a way that within each of the multiple bubbles at least two streams of electrons cross, thereby resulting in electron modulation in each of the multiple plasma bubbles and formation of a modulated electron bunch in each of the multiple plasma bubbles.

A radiation source as claimed in claim 2 or claim 3, wherein the laser-plasma wakefield accelerator is set up to cause the or each modulated electron bunch to radiate inside the or each plasma bubble, thereby to cause emission of coherent radiation within the or each bubble and subsequent emission of the coherent radiation from the or each bubble.

A radiation source as claimed in claim 1 further comprising a modulator for modulating the plasma density in the vicinity of the at least one bubble, so that the plasma electrons injected into the at least one bubble comprise a pre- modulated electron bunch.

A radiation source as claimed in claim 5 wherein the laser-plasma wakefield accelerator is arranged to form at least one relativistic reflector at the back of the at least one bubble.

7. A radiation source as claimed in claim 5 wherein the relativistic reflector is arranged to cause a Lorentz contraction of the at least one modulated electron bunch, and betatron motion of the at least one modulated electron bunch causes emission of radiation within the at least one bubble.

8. A radiation source as claimed in claim 1 wherein the laser-plasma wakefield accelerator is configured to allow the at least one modulated electron bunch to be emitted from at least one bubble.

9. A radiation source as claimed in claim 8 comprising a radiator downstream of the bubble for causing the at least one modulated electron bunch to emit coherent radiation.

10. A method that uses a laser-plasma wakefield accelerator, the method comprising: passing at least one laser pulse through a plasma to generate a wake of evacuated plasma bubbles; injecting at least one stream of plasma electrons into at least one bubble in the wake of evacuated plasma bubbles; modulating at least one electron stream before or after injection into at least one plasma bubble to form at least one modulated electron bunch; and causing the modulated electron bunch to radiate, thereby to generate radiation.

1 1. A method as claimed in claim 10 involving causing the laser-plasma wakefield accelerator to simultaneously inject at least two streams of electrons into at least one bubble, in such a way that they cross at the rear of the bubble, thereby to cause electron modulation inside at least one plasma bubble and formation of the at least one modulated electron bunch.

12. A method as claimed in claim 1 1 involving setting up the laser-plasma wakefield accelerator to cause the at least one modulated electron bunch to radiate inside at least one plasma bubble, thereby to cause emission of coherent radiation within the bubble.

13. A method as claimed in claim 10 involving using a modulator for modulating the plasma density in the vicinity of the bubbles, so that the plasma electrons injected into at least one bubble comprise a pre-modulated electron bunch.

14. A method as claimed in claim 13 involving forming a relativistic reflector at the back of at least one bubble.

15. A method as claimed in claim 14 wherein the relativistic reflector is arranged to cause a Lorentz contraction of the pre-modulated electron bunch and subsequent betatron motion of the modulated electrons causes the emission of coherent radiation from within the at least one bubble.

16. A method as claimed in claim 10 involving allowing the at least one modulated electron bunch to be emitted from at least one bubble.

17. A method as claimed in claim 16 involving using a radiator to cause the modulated electron stream to emit radiation.

18. A method as claimed in claim 17 wherein the radiator comprises an undulator, a laser beam or another laser-plasma wakefield accelerator bubble.

19. A method as claimed in any of claims 10 to 18 comprising using the radiation emitted.

20. A method as claimed in any of claims 10 to 19 comprising varying the wavelength of the radiation emitted by varying the plasma density.