All-Optical control of electron trapping in plasma channels

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1 University of Nebraska - Lincoln From the SelectedWorks of Serge Youri Kalmykov Fall September 15, 13 All-Optical control of electron trapping in plasma channels Serguei Y. Kalmykov, University of Nebraska-Lincoln Bradley A. Shadwick, University of Nebraska-Lincoln Xavier Davoine Available at:

2 All-Optical Control of Electron Trapping in Plasma Channels Serguei Y. Kalmykov and Bradley A. Shadwick Department of Physics and Astronomy, University of Nebraska Lincoln Lincoln, Nebraska Xavier Davoine CEA, DAM, DIF Arpajon F-9197, France Abstract The accelerating bucket of a laser-plasma accelerator (a cavity of electron density maintained by the laser pulse radiation pressure) evolves slowly, in lock-step with the optical driver, and readily traps background electrons. The trapping process can thus be controlled by purely optical means. Sharp gradients in the nonlinear refractive index produce a large frequency red-shift, localized at the leading edge of the pulse. Negative group velocity dispersion associated with the plasma response compresses the laser pulse into a relativistic optical shock (ROS), slowing the pulse (and the bucket), reducing the electron dephasing length, and limiting energy gain. Even more importantly, the ponderomotive force of the ROS causes the bucket to constantly expand, trapping copious unwanted electrons, polluting the electron spectrum with a high-charge, low-energy tail. We show that using a drive pulse with a bandwidth close to a one-half of the carrier wavelength provides effective dispersion compensation. The negatively chirped, ultrahigh bandwidth (up to nm) drive pulse: prevents ROS formation through dephasing; extends the dephasing length; and almost completely suppresses continuous injection. High quality, GeV-scale electron beams can be thus produced with sub-1 TW lasers (rather than PW-class) in mm-scale (rather than cm-scale), high-density plasmas. ROS formation can be further delayed by using a plasma channel to suppress diffraction of the pulse leading edge, minimizing longitudinal variations in the pulse. At the same time, the combination of a bubble (a selfconsistently maintained, soft hollow channel) and a preformed wide channel forces transverse flapping of the laser pulse tail, causing oscillations of the bubble size. The resulting periodic injection produces a polychromatic beam that consists of a number of background-free quasi-monoenergetic components. The number of these components, their charge, energy, and energy difference can be controlled by changing the channel radius and acceleration distance, whereas negative chirp of the driver suppresses the background and boosts their energy. Such clean polychromatic beams can be an asset for tunable X-ray table-top sources. I. INTRODUCTION The radiation pressure of a sub-1 fs, multi-terawatt laser pulse propagating in an underdense plasma creates complete electron cavitation, leaving the background ions unperturbed [1], []. The resulting bubble of electron density guides the pulse over many Rayleigh lengths while maintaining GV/cmscale accelerating and focusing gradients [3]. The shape of the bubble evolves slowly, in lock-step with the optical driver, making it possible to trap initially quiescent background electrons, eliminating the need for the external photocathode [] []. This compact laser-plasma accelerator (LPA) produces tunable, GeV-scale energy, 1-1 pc quasi-monoenergetic n e (norm.) 1 Peak intensity (norm.) r (µm) Fig. 1. Radial profile of electron density (left axis) and normalized intensity of the NCP in a cross-section taken at the peak intensity (right axis). (WAKE simulation.) Density on axis n e(r = ) = cm 3. Blue curve: initial distribution of intensity (z =, matched spot). Red curves: distributions of intensity during the self-guided stage, at z = mm (thin solid line) and.5 mm (thick dashed line). At the later stage of propagation, the spot size is nearly one-half of the channel-matched radius, and changes very little. (QME) electron bunches from sub-cm-length plasmas [9], [1]. Energy gain and beam quality competitive with standard linear accelerators, and, more importantly, flexibility in electron beam formats (inaccessible to standard linacs) make the LPA attractive for various scientific and technological applications [11], [1]. This flexibility is rooted in the nature of the driver a relativistically intense laser pulse. The nonlinear dynamics of the driver can be controlled by properly shaping the initial phase and amplitude in order to enhance or compensate for nonlinear optical (NLO) effects, thus controlling electron selfinjection by purely optical means, thereby adjusting the properties of electron beams to the demands of a given application. The miniature LPA, driven by a compact, high-repetitionrate terawatt laser, has become a popular research tool and a driving force of many discoveries in the university labs. Yet, the growing demand for higher electron energies (e.g. for the design of compact X-ray sources [13], [1]) offsets the main advantage of the LPA its compactness. Per standard scalings [3], reaching beyond GeV requires cm-length plasmas and petawatt-power lasers []. Limited availability of the latter, in combination with their low repetition rate and poor beam quality [15] [17], presently inhibits progress in the field. Increase in the size of the experiment also complicates predictive modeling [1]. In this Report, we propose one way to obtain GeV-scale, high-quality electron beams in formats interesting for applications without increasing the laser power or the size of the experiment. We rely on a standard target design (a density channel) and, more importantly, on manipulations of the laser phase [], [19]. The purpose of this photon engineering is to provide a proper dispersion control in order to suppress.5

3 dn/de (1 7 MeV 1 ) E (GeV) Fig.. Electron beam quality control in the uniform plasma []. The 7 TW driver pulse (TLP or NCP) has 3 fs duration; n = cm 3. In the TLP case, energy spectra are shown near the end of the density plateau, z =. mm (black), and in the NCP case at z = 1. mm (blue) and. mm (red). In the TLP case, the highest energy electrons, E.5 GeV, are at dephasing. The NCP allows reaching this energy in a 5% shorter plasma, and with a very insignificant tail (cf. blue vs black curve). The tail remains suppressed through the rest of the plasma (cf. red vs black curve). The negative chirp of the driver eventually boosts the QME bunch energy by 3%, and the brightness by a factor.5. detrimental NLO effects and prevent unfavorable scenarios of the bubble evolution. As a result, QME electron beams accelerated through dephasing receive an energy boost and, at the same time, remain mostly free of low-energy background. Electron beam degradation seen in experiments [15], [1] is caused by the driver pulse transformation into a relativistic optical shock (ROS). This NLO process is the same as the soliton effect occurring in optical fibers [], [1]. As the relativistically intense pulse self-guides in the blowout regime, its leading edge constantly witnesses the down-ramp of a nonlinear refractive index. Resulting phase self-modulation (PSM) red-shifts the laser frequency at the location of the index gradient, introducing a constantly increasing positive frequency chirp. Negative group velocity dispersion (GVD) associated with the plasma response slows down the red-shifted frequency components, building up intensity at the leading edge, creating a sharp front with a rise time 1/ω (here, ω = πc/λ is the carrier frequency of the pulse, c is a speed of light in vacuum, and λ is the carrier wavelength). Pulse self-steepening slows down the bubble, reducing the dephasing length and limiting the energy gain [3]. In the dense plasma, n > 1 1 cm 3, the frequency downshifts by a large fraction of ω long before electron dephasing. Concurrent selfcompression of the pulse forces elongation of the bubble []. Continuous injection ensues, which beam loading is unable to terminate, polluting the electron beam with a high-charge, low-energy tail [] []. To suppress the tail, we propose to delay the ROS formation using a dispersion compensation technique similar to that employed in fiber optics, compensating for the nonlinear reduction in frequency (exceeding ω /) with a proper choice of the initial laser phase. To be practically effective, this approach needs broad frequency spectrum amplifiers delivering few-joule, near-ir laser pulses with bandwidth approaching one-half of the carrier wavelength (such as a Petawatt Field Synthesizer, or PFS, presently under development in MPI für Quantenoptik []). By temporally advancing the high frequency components of the incident pulse (i.e. introducing a negative frequency chirp), we reduce the positive chirp produced by the PSM. The negatively chirped pulse (NCP) thus remains uncompressed through dephasing, continuous injection remains suppressed, and the QME electron bunch dn / de (1 7 MeV 1 ) E (GeV) 1 1 (a) (b) Fig. 3. Energy spectra for electrons accelerated with the TLP (black) and NCP (red) in a channel, (a) z =. mm; (b). mm; (c). mm. Vertical scale is the same as in Fig.. The spectrum is polychromatic, with well separated energy peaks. Consecutive injections into the first bucket yield peaks 1(1 ) and ( ). In the NCP case, electrons from the second bucket form the lowestenergy peak 3 with E.7 GeV, situated on top of the broad distribution produced by the continuous injection into the first bucket; negative chirp of the driver keeps this background low. In the TLP case, the lowest-energy peak is the part of the continuously injected electron population [cf. Fig. 5(b)]. In the NCP case, the energy spread of the peaks is preserved; their average energy and energy difference is controlled by changing the acceleration distance. Beams statistics for panel (c) is shown in Table I. remains dominant. As a bonus, the higher average frequency of the pulse, together with slower etching of its front, effectively increases the dephasing length, further boosting electron energy [], [19]. We show in this Report that this technique of dispersion compensation, combined with manipulations of a plasma target, helps produce high-quality electron beams in formats other than a single QME bunch. Propagating the NCP in a wide leaky plasma channel [3] suppresses diffraction of its leading edge, further reducing its self-steepening. For the laser and plasma parameters of Ref. [], the combination of the chirp and the channel boosts final electron energy from.5 to.75 GeV over less than a mm acceleration length. In addition, the channel introduces periodic oscillations of the bubble size, bringing about periodic self-injection []. The resulting polychromatic electron beams consist of several high-quality, QME components each carrying 1 pc-scale charge. The number of these components can be controlled by varying the channel radius, whereas their mean energy and energy separation is controlled by changing the plasma length [5]. Negative chirp minimizes the noise (continuous energy background), improving spectral separation and energy spread of individual components. Such clean multi-color beams, inaccessible to standard accelerator technology, may find a unique application as drivers for tabletop tunable short-pulse X- and gamma-ray sources [13], [1]. II. SIMULATION METHODS Physical processes underlying all-optical manipulations of the LPA are explored using a combination of reduced and full particle-in-cell (PIC) simulations. Fast, computationally cheap (c)

4 TABLE I. STATISTICS OF QME ELECTRON BEAMS [FIG. 3(C)] TABLE II. STATISTICS OF ENERGY TAILS [FIGS. AND 3(C)] Beam 1 Beam 1 Beam Beam Beam 3 a Q (nc) a E max (MeV) σ(α) (mrad) F (MeV 1 ) b Q (pc) E (MeV) σ N E (%) ε N (mm mrad) σ(α) (mrad) F b B c a with the background filtered out b in 1 7 electrons MeV 1 c in 1 11 electrons MeV 1 mm mrad. quasistatic simulations using the fully relativistic, cylindrically symmetric, time-averaged (over a period 1/ω ) code WAKE [1] explain dynamics of the ROS formation. These simulations shed light on the electron plasma response to the ROS and explain the physical nature of the continuous injection caused by the laser pulse self-compression. The laser pulse phase profile sufficient to disrupt ROS formation is also recovered from these simulations. These details (partly reported in Ref. []) shall be published elsewhere. Here, we report on the kinetics of electron self-injection and the effect of the chirp and the channel on the electron beam phase space volume. These results are obtained from fully dynamic, three-dimensional (3D) PIC simulations using the fully explicit, quasi-cylindrical code CALDER-Circ [1], []. Grid spacings and number of particles per cell in these simulations are specified in []. These are sufficient to maintain low sampling noise and negligibly low numerical dispersion. All figures and tables, except Fig. 1, show the results of CALDER-Circ simulations. III. A. Initial Conditions RESULTS AND DISCUSSION Our simulations correspond to the interaction regime earlier considered in []. The linearly polarized, 7 TW pulse is focused at the plasma entrance, and then propagates toward positive z. The complex amplitude of the vector potential is a(z = ) = a exp[ (r/r ) ln (t/τ L ) + iφ(t)]. Here, a = 3.7, τ L = 3 fs, r = 13. µm, and λ =.5 µm. The rate of the phase variation defines the instantaneous frequency, ω(t) = dφ/dt = ω + ( ln )σ(κ/τ L ) t. Simulations with a 3 fs-length, transform-limited pulse, or TLP (κ = ), are further referred to as the reference case []. To combat the ROS formation, we temporally advance high frequencies (σ = 1) and increase the bandwidth by a factor of (κ =.33), keeping other parameters unchanged; the NCP in this format may be obtained by under-compressing a -TW, 5-fs pulse of the future PFS []. The plasma spans between z = and 3 mm; it has.5 mm-length linear entrance and exit ramps, and a mm longitudinally flat section with n e (r = ) = cm 3. A detailed comparative study of the TLP and NCP evolution in a uniform plasma was presented in []. In this Report, we complement that study by placing the the pulse in a plasma channel in order to suppress diffraction of its leading edge, further mitigating self-steepening and obtaining, as a bonus, new features in the Reference case TLP in channel NCP in channel c a charge in the energy range 5 MeV < E < E max b average flux, F = e 1 Q/ E, E = E max 5 MeV c with electrons of beam 3 filtered out. electron beam. The leaky channel used in simulations has the radial density profile shown in Fig. 1: n (1 + r /rch), for r r ch n e (r) = n ( r/r ch ), for r ch < r r ch (1), for r > r ch Results presented below correspond to the channel matched to the spot size of the incident pulse [3] (but not to the selfguided spot size). This choice appears to be optimal from the standpoint of beam quality. B. Electron Energy Spectra According to Fig., the negative chirp of the driver remarkably improves the beam quality in a uniform plasma by suppressing the energy tail; maintaining quasi-monoenergetic acceleration through dephasing; and increasing the energy gain (beam statistics for this case can be found in []). Propagating the pulse in a channel suppresses diffraction of the leading edge, further mitigating self-steepening. Figure 1 indicates that cooperation of the linear refraction of the channel and the nonlinear self-focusing keeps the most intense part of the pulse (i.e. its head) guided with an almost unchanging spot. Importantly, by stabilizing the dynamics of the pulse leading edge, the channel also destabilizes the dynamics of its tail. The tail is confined inside the bubble a narrow, soft hollow channel with the radius much smaller (and index contrast much higher) than that of the wide preformed parabolic channel. Even without a channel, the tail flaps radially, driving the bubble boundaries sidewards, causing bubble to expand and self-inject electrons [7]. In a transversely uniform plasma this flapping subsides, and the injection resumes only when the ROS forms. The channel enhances the flapping, causing a number of distinct consecutive injections (in contrast to the single injection in the uniform plasma). In our simulations, regardless of the chirp, injection into the first bucket occurs twice, adding lower-energy QME components [beams and in Fig. 3(c)]. 1 Statistics of these multi-component beams are presented in Tables I and II. Table I summarizes properties of the QME components, whereas Table II compares the noise levels created by the continuous injection. Table I shows: the total charge, Q; mean energy, E ; normalized energy spread, σe N = σ E/ E, where σ E is the dispersion of energy; root-mean-square (RMS) normalized transverse emittance, ε N = 1/ [(ε N x ) + (ε N y ) ] 1/, where ε N i = (m e c) 1 [( p i p i )( ri r i ) ( p i r i r i p i ) ] 1/ ; and RMS divergence σ(α) = 1/ [σx(α) + σy(α)] 1/, where σ i (α) = p z 1 ( p i p i ) 1/. We also 1 The channel radius defines the number of bubble size oscillations, and thus the number of spectral components in the beam. A narrower channel generates more energy components, but also more background [5].

5 show the peak flux F extracted from Fig. 3(c) and average brightness, proportional to the particle density in the phase space, B F (m e c ) E (ε N ). These quantities are commonly used in beam physics to assess the quality of the particle source [1], []. Negative chirp of the driver extends the dephasing length for electrons injected into the first bucket [beams 1 and of Fig. 3(c)] and preserves electrons accelerated in the second bucket [beam 3 of Fig. 3(c)]. In the TLP case, the highestenergy beam 1 dephases around z =. mm. In contrast, acceleration with the NCP carries on through the rest of the plasma, boosting the beam 1 energy by 5%, and beam energy by 3%. The energy spread of these peaks (full width at half-maximum) drops nearly by half, and remains mostly unchanged throughout acceleration. Their charge remains in the 1-pC range. As a result, the brightness of the beam 1() nearly doubles (triples). Furthermore, the too-slowlyexpanding first bucket [cf. Fig. (a)] is unable to absorb electrons self-injected into the second bucket. This component, making up the beam 3 of Fig. 3(c), is clearly seen in the longitudinal phase space in Fig. 5(c). Early dephasing (around z = mm) limits its energy to.3 GeV, whereas the charge and brightness are close to those of beam. By the end of acceleration,.75% of the NCP energy is transferred to the QME beams 1 3. Figure 3 shows that the energy of individual beams and their energy separation can be controlled by changing the acceleration length. Importantly, owing to the stabilizing effect of the chirp, the acceleration distance can be varied safely, without accumulation of the low-energy background. Reduction of the background is quantified in Table II. In the reference case, the energy tail contains about 7% of the total charge accelerated above 5 MeV []. The combination of the negative chirp and the channel reduces both continuously injected charge and the flux in the tail roughly by a factor 3.7. The channel alone is unable to suppress the tail, which remains as bright as in the reference case. C. Kinetics of Electron Self-Injection 1) Laser Pulse Evolution (WAKE Simulations): The combination of chirp and channel delays the ROS formation as expected. In the reference case, by the end of the interaction, red-shifted mid-ir photons slide inside the bubble, mixing with the frequency-unshifted radiation. This photon phase space rotation [19] compresses the pulse to 1.5 cycles, with a % reduction in average frequency and energy. Temporal advancement of high frequencies in the NCP case partly compensates for the nonlinear red shift, slowing down the photon phase space rotation. The red-shift remains localized at the pulse leading edge, yielding only % reduction in the pulse average frequency. Even though the negative GVD still slows down the red-shifted frequency components, etching away the pulse front, the build-up of the field amplitude becomes noticeable only at the end of the interaction. Even then the pulse is not fully compressed and is far from depletion (total energy loss is about %). Placing the pulse into a channel suppresses diffraction of the leading edge, reducing the pulse steepening even further. ) Evolution of the Bubble and Dynamics of Self-Injection in a Channel (CALDER-Circ Simulations): Figure links the process of self-injection with the evolution of the bubble. Fig.. Bubble size evolution and electron injection in the reference case (black) and in the case of NCP propagating in a channel (red). The density plateau spans between z =.5 and.5 mm. (a) Length of the accelerating phase on axis vs propagation length. The NCP in a channel self-compresses very slowly. Thus, in contrast to the reference case, the bubble expands insignificantly. (b) (d) Macroparticle tracking data from the electron phase space at z =. mm (only particles with E > 5 MeV are shown). (b) Collection volume (initial radial offset vs initial longitudinal position). (c) Longitudinal collection phase space (final longitudinal momentum vs initial longitudinal position). In a channel, the bubble size oscillates twice between z =. and 1. mm, producing two distinct groups of QME electrons. These are the beams 1 and of Fig. 3(c). Blue ellipses encircle particles injected into the second bucket. A compact group of red markers (with p z 7 GeV/c and.5 mm < z in <. mm) in panel (c) corresponds to the QME beam 3 of Fig. 3(c). (d) Transverse collection phase space (initial radial offset vs final longitudinal momentum). Injection occurs from a cylindrical shell with a local radius close to the spot size of the laser pulse head; there is no evidence of longitudinal injection from the near-axis region [9]. The channel stabilizes the evolution of the pulse leading edge. Hence, the collection radius [red markers in panels (b) and (d)] remains almost constant through the entire interaction. The bubble size is defined as the length of the accelerating phase on the axis (viz. the length of the region inside the bubble where the longitudinal electric field is negative). In all cases considered here, the highest-energy QME bunch (having over 15 pc charge) forms early, during the first oscillation of the bubble. In the reference case, self-compression of the pulse initiates expansion of the bubble after z = 1. mm; the resulting continuous injection ruins the beam. Evolution of the bubble driven by the NCP in the channel is noticeably different. The two periods of bubble size oscillations clearly seen in Fig. (a) cause two consecutive injections into the first bucket [cf. Figs. (b) and (c)]. First injection occurs between z =. and.95 mm, and the second one between z = 1. and 1. mm, producing QME beams 1 and of Fig. 3(c). Figure (c) shows that weak expansion of the bubble between z = 1.5 and.5 mm still produces the energy tail, but statistics tells us that its flux is only 5% of that in the reference case.

6 Fig. 5. Producing clean polychromatic electron beams with the NCP in a wide leaky plasma channel. Pulse propagates to the right. Snapshots of density (top row) and longitudinal phase space (bottom) are shown at the end of the density plateau. Column (a): acceleration through dephasing in the reference case. The bubble elongates and becomes strongly non-axisymmetric. Continuous injection is in progress. A massive, bright energy tail (γ e < 9) dominates electron spectrum. Column (b): acceleration through dephasing with the TLD pulse in the channel. The channel suppresses pulse head diffraction, reducing expansion of the bubble. The channel also brings about periodic self-injection producing a pair of distinct QME bunches. The energy gain, however, is only marginally higher than in the reference case, and the energy tail (γ e < 5) remains as bright. Column (c): acceleration with the NCP in a channel. Introduction of the chirp (in combination with the channel) suppresses the bubble expansion nearly by half. The energy tail is suppressed: its charge and flux drop by a factor 3.7 against the reference case. The second wake bucket is not destroyed, producing additional QME electron bunch. The highest-energy electrons from the first bucket are far from dephasing. They receive 5% energy boost against the reference case, reaching 75 MeV energy over 1. mm acceleration distance. In addition, the NCP favors acceleration of electrons in the second bucket. In both cases shown in Fig., the second bucket starts expanding and trapping electrons around z =.5 mm. Injection into the first bucket destroys the sheath of the second bucket, effectively terminating injection around z =. mm. Injection into the second bucket never resumes, and the electron bunch [beam 3 of Fig. 3(c)] remains highly monoenergetic (cf. Table I). In the absence of the chirp, this bunch is eventually swallowed by the expanding first bucket and thus contributes to the background [cf. Figs. 5(a) and 5(b)]. The chirp, however, slows down expansion of the first bucket [compare, e.g. Figs. 5(c) and 5(a)]. Electrons in the second bucket, clearly seen in the density distribution and the longitudinal phase space in Fig. 5(c), are thus accelerated through dephasing, adding another QME component to the electron energy distribution. The collection volume and transverse collection phase space in Figs. (b) and (d) show that, in all instances, whether self-injection is continuous or periodic, into the first or the second bucket, in a uniform plasma or in a channel, all electrons are injected from the sheath, as predicted by the theory [], [], []. Electrons accelerated through the end of the plasma are all collected from the cylindrical shell. The collection radius is close to the laser spot radius taken at the pulse head (viz. the most intense part of the pulse). There is no evidence of longitudinal injection reported earlier for a similar regime [9]. The collection radius in a channel is remarkably uniform. Therefore, in agreement with Fig. 1, the evolution of the most intense part of the pulse (its head) is stabilized throughout the entire interaction. Even though the pulse head remains unmatched for the channel (cf. Fig. 1), its diffraction is suppressed entirely, showing no signs of betatron oscillations. This fact, as well as the collection volume uncharacteristic of the longitudinal wavebreaking, rules out parametric resonance and periodic longitudinal wavebreaking [], [5] as a cause of periodic injection. IV. CONCLUSION Numerical simulations presented in this Report demonstrate production of clean, multi-color, GeV-scale electron beams (a beam format inaccessible to standard acceleration techniques) in a miniature, mm-size LPA. Control of electron beam properties is achieved by purely optical means, using manipulations of the phase of the incident laser pulse in order to compensate large nonlinear frequency shifts ( ω ω ) imparted by the relativistic mass effect and wake excitation. Anticipating exciting developments in the laser technology leading to 1 TW-class pulses of a sub--cycle duration [], we demonstrate the advantage of their ultra-wide bandwidth for all-optical control of electron beam quality in the blowout regime of laser-plasma acceleration. Under-compressing the pulse and temporally advancing higher frequencies (i.e. introducing a negative chirp) compensate for the frequency redshift produced by wake excitation. This prevents rapid selfcompression of the pulse and keeps the dark current low over the entire dephasing length. Propagating the pulse in a channel suppresses diffraction of the pulse leading edge, further reducing pulse self-steepening and bubble expansion, delaying dephasing of electrons, boosting beam energy. Simulations presented in this Report, demonstrate a 5% boost (from.5

7 to.75 GeV), with the full acceleration distance being less than mm. Transverse dynamics of the pulse in the channel causes periodic injection, producing a polychromatic electron beam. Negative chirp of the driver minimizes the amount of noise (continuous energy background), keeping QME spectral components well separated. The channel radius is an important parameter, controlling the number of spectral components in the beam, whereas their energy and energy difference can be controlled by changing the plasma length. Low energy spread and clear separation of GeV-scale spectral components in energy, as well as a minimal amount of noise (resulting from all-optical control of self-injection), make our beams attractive for advanced radiation sources. They can drive compact, all-optical, multi-color inverse Compton gamma-ray sources [1]. Alternatively, by separating the QME components in a magnetic electron spectrometer and using post-manipulations with the beam delay lines, or selectively focusing them with highly chromatic magnetic quadrupole lenses [3], one can use our multi-color beams as drivers of compact, tunable, synchronized, pulsed broad-bandwidth X- ray sources [13]. ACKNOWLEDGMENT The work of SYK and BAS is supported by the U.S. DOE Grant DE-SC3, NSF Grant PHY-113, and DOD AFOSR Grant FA The CALDER-Circ simulations were performed using HPC resources of GENCI- CCRT and GENCI-CINES (grant ). REFERENCES [1] P. Mora and T. M. Antonsen, Jr., Electron cavitation and acceleration in the wake of an ultraintense, self-focused laser pulse, Phys. Rev. E, vol. 53, no. 3, pp. R-R71, Mar [] A. Pukhov and J. Meyer-ter-Vehn, Laser wake field acceleration: the highly non-linear broken-wave regime, Appl. Phys. B: Lasers Opt., vol. 7, no. -5, pp , Apr.. [3] W. 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