Relativistic Ionization Front Research Articles

Development of the self-modulation instability of a relativistic proton bunch in plasma

Self-modulation is a beam–plasma instability that is useful to drive large-amplitude wakefields with bunches much longer than the plasma skin depth. We present experimental results showing that, when increasing the ratio between the initial transverse size of the bunch and the plasma skin depth, the instability occurs later along the bunch, or not at all, over a fixed plasma length because the amplitude of the initial wakefields decreases. We show cases for which self-modulation does not develop, and we introduce a simple model discussing the conditions for which it would not occur after any plasma length. Changing bunch size and plasma electron density also changes the growth rate of the instability. We discuss the impact of these results on the design of a particle accelerator based on the self-modulation instability seeded by a relativistic ionization front, such as the future upgrade of the Advanced WAKefield Experiment.

Efficient generation of tunable magnetic and optical vortices using plasmas

Plasma is an attractive medium for generating strong microscopic magnetic structures and tunable electromagnetic radiation with predictable topologies due to its extraordinary ability to sustain and manipulate high currents and strong fields. Here, using theory and simulations, we show efficient generation of multimegagauss magnetic and tunable optical vortices when a sharp relativistic ionization front (IF) passes through a relatively long wavelength Laguerre-Gaussian (LG) laser pulse with orbital angular momentum (OAM). The optical vortex is frequency upshifted within a wide spectral range simply by changing the plasma density and is compressed in duration. The topological charges of both vortices can be manipulated by controlling the OAM mode of the incident LG laser and/or by controlling the topology and density of the IF. For relatively high (low) plasma densities, most of the energy of the incident LG laser pulse is converted into the magnetic (optical) vortex, with conversion efficiency approaching ∼90% for an ideal IF.Received 13 April 2022Revised 11 August 2022Accepted 2 January 2023DOI:https://doi.org/10.1103/PhysRevResearch.5.L012011Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLaser-plasma interactionsMagnetic field generation & plasma dynamoOptical vorticesX-ray generation in plasmasPlasma PhysicsAccelerators & BeamsAtomic, Molecular & Optical

Transition between Instability and Seeded Self-Modulation of a Relativistic Particle Bunch in Plasma.

We use a relativistic ionization front to provide various initial transverse wakefield amplitudes for the self-modulation of a long proton bunch in plasma. We show experimentally that, with sufficient initial amplitude [≥(4.1±0.4) MV/m], the phase of the modulation along the bunch is reproducible from event to event, with 3%-7% (of 2π) rms variations all along the bunch. The phase is not reproducible for lower initial amplitudes. We observe the transition between these two regimes. Phase reproducibility is essential for deterministic external injection of particles to be accelerated.

Ultra-short pulse generation from mid-IR to THz range using plasma wakes and relativistic ionization fronts

This paper discusses numerical and experimental results on frequency downshifting and upshifting of a 10 μm infrared (IR) laser to cover the entire wavelength (frequency) range from λ = 1 to 150 μm (ν = 300–2 THz) using two different plasma techniques. The first plasma technique utilizes frequency downshifting of the drive laser pulse in a nonlinear plasma wake. Based on this technique, we have proposed and demonstrated that in a tailored plasma structure, multi-millijoule energy, single-cycle, long-wavelength IR (3–20 μm) pulses can be generated by using an 810 nm Ti:sapphire drive laser. Here, we extend this idea to the THz frequency regime. We show that sub-joule, terawatts, single-cycle terahertz (2–12 THz or 150–25 μm) pulses can be generated by replacing the drive laser with a picosecond 10 μm CO2 laser and a different shaped plasma structure. The second plasma technique employs frequency upshifting by colliding a CO2 laser with a rather sharp relativistic ionization front created by ionization of a gas in less than half cycle (17 fs) of the CO2 laser. Even though the electrons in the ionization front carry no energy, the frequency of the CO2 laser can be upshifted due to the relativistic Doppler effect as the CO2 laser pulse enters the front. The wavelength can be tuned from 1 to 10 μm by simply changing the electron density of the front. While the upshifted light with 5<λ(μm)<10 propagates in the forward direction, that with 1<λ(μm)<5 is back-reflected. These two plasma techniques seem extremely promising for covering the entire molecular fingerprint region.

Seeding self-modulation of a long proton bunch with a short electron bunch

We briefly compare in numerical simulations the relativistic ionization front and electron bunch seeding of the self-modulation of a relativistic proton bunch in plasma. When parameters are such that initial wakefields are equal with the two seeding methods, the evolution of the maximum longitudinal wakefields along the plasma is similar. We also propose a possible seeding/injection scheme using a single plasma that we will study in upcoming simulations works.

Determination of the Charge per Micro-Bunch of a Self-Modulated Proton Bunch using a Streak Camera

The Advanced Wakefield Experiment (AWAKE) develops the first plasma wakefield accelerator with a high-energy proton bunch as driver. The 400 GeV bunch from CERN Super Proton Synchrotron (SPS) propagates through a 10 m long rubidium plasma, ionized by a 4TW laser pulse co-propagating with the proton bunch. The relativistic ionization front seeds a self-modulation process. The seeded self-modulation transforms the bunch into a train of micro-bunches resonantly driving wakefields. We measure the density modulation of the bunch, in time, with a streak camera with picosecond resolution. The observed effect corresponds to alternating focusing and defocusing fields. We present a procedure recovering the charge of the bunch from the experimental streak camera images containing the charge density. These studies are important to determine the charge per micro-bunch along the modulated proton bunch and to understand the wakefields driven by the modulated bunch.

Evidence of radial Weibel instability in relativistic intensity laser-plasma interactions inside a sub-micron thick liquid target

Super-intense laser plasma interaction has shown great promise as a platform for next generation particle accelerators and sources for electron, x-rays, ions and neutrons. In particular, when a relativistic intense laser focus interacts with a thin solid density target, ionized electrons are accelerated to near the speed of light (c) within an optical cycle and are pushed in the forward and transverse directions away from focus, carrying a significant portion of the laser energy. These relativistic electrons are effectively collisionless, and their interactions with the ions and surrounding cold electrons are predominantly mediated by collective electromagnetic effects of the resulting currents and charge separation. Thus, a deeper understanding of subsequent high energy ions generated from various mechanisms and their optimization requires knowledge of the relativistic electron dynamics and the fields they produce. In addition to producing MV/m quasi-static fields, accelerating the ions and confining the majority of the electrons near the bulk of the laser target, these relativistic electron currents are subject to plasma instabilities like the Weibel instability as they propagate through the thermal population in the bulk target. In this work, we present high temporal (100 fs) and spatial (1 μm) resolution shadowgraphy video capturing relativistic radial ionization front expansion and the appearance of filamentation radiating from the laser spot within a sub-micron thick liquid sheet target. Filamentation within the region persists for several picoseconds and seeds the eventual recombination and heating dynamics on the nanosecond timescale. A large scale three-dimensional particle-in-cell (PIC) simulation of the interaction revealed the presence of strong magnetic fields characteristic of Weibel Instability, and corroborated the relativistic radial expansion of the ionization front, whose speed was determined to be 0.77c. Both the experimental and simulation results strongly point towards the target field ionization and the outward expanding hot electron current as the cause of the radial expansion.

Particle-in-cell simulation for frequency up-conversion of microwave to terahertz radiation by a relativistic hollow ionization front

The interaction of an electromagnetic wave with a relativistic ionization front with frequency up-conversion has been demonstrated by the particle-in-cell (PIC) method. In the PIC simulation, the plasma ionization front is formed by using an electron beam ionizing the background gas. The PIC results are in good agreement with the basic analytic theory. In addition, the charged particles are modulated in the interaction area observed in the PIC simulation, which is hardly obtained by other methods. Based on the verified PIC methods, a relativistic hollow ionization front for frequency up-conversion of microwave to terahertz radiation is proposed for increasing the reflection cross section. Finally, the reflected energy can be increased by at least 3 orders of magnitude compared to the traditional methods.

Experimental Observation of Proton Bunch Modulation in a Plasma at Varying Plasma Densities.

We give direct experimental evidence for the observation of the full transverse self-modulation of a long, relativistic proton bunch propagating through a dense plasma. The bunch exits the plasma with a periodic density modulation resulting from radial wakefield effects. We show that the modulation is seeded by a relativistic ionization front created using an intense laser pulse copropagating with the proton bunch. The modulation extends over the length of the proton bunch following the seed point. By varying the plasma density over one order of magnitude, we show that the modulation frequency scales with the expected dependence on the plasma density, i.e., it is equal to the plasma frequency, as expected from theory.

Generation of sub-terahertz radiation using the DC-to-AC radiation converter

The operation of the DC-to-AC radiation converter (DARC) in the sub-THz region is confirmed. A relativistic ionization front which is created by a loosely focused of Ti:sapphire laser pulse propagating through a capacitor array of period d = 0.2 cm with a gas pressure between 1 and 200 Pa. The maximum frequency of the generated emission is determined to be in the range of 0.1 to 0.3 THz by using several diodes.

Relativistic Runaway Ionization Fronts

We investigate the first example of self-consistent impact ionization fronts propagating at relativistic speeds and involving interacting, high-energy electrons. These fronts, which we name relativistic runaway ionization fronts, show remarkable features such as a bulk speed within less than one percent of the speed of light and the stochastic selection of high-energy electrons for further acceleration, which leads to a power-law distribution of particle energies. A simplified model explains this selection in terms of the overrun of Coulomb-scattered electrons. Appearing as the electromagnetic interaction between electrons saturates the exponential growth of a relativistic runaway electron avalanche, relativistic runaway ionization fronts may occur in conjunction with terrestrial gamma-ray flashes and thus explain recent observations of long, power-law tails in the terrestrial gamma-ray flash energy spectrum.

High-brilliance synchrotron radiation induced by the plasma magnetostatic mode

Using multi-dimensional PIC simulations we show that the magnetic undulator-type field of the plasma magnetostatic mode is indeed produced by the interaction of a laser pulse with a relativistic ionization front, as predicted by linear theory for a cold plasma. When the front with this magnetostatic mode is followed by a relativistic electron beam, the interaction of the beam with this magnetic field, produces FEL-type synchrotron radiation, providing a direct signature of the magnetostatic mode. The possibility of generating readily detectable ultrashort wavelength radiation using this mode, by employing state-of-the-art laser systems, is demonstrated, thus opening the way towards experimental observation of the hitherto unseen magnetostatic mode and the use of this plasma FEL mechanism to provide a source of high-brilliance ultrashort wavelength radiation.

Relativistic effects in radar detection of ionization fronts produced by ultra-high energy cosmic rays

We revisit the radar echo technique as an approach to detect ultra-high energy cosmic rays (UHECR). The UHECR extensive air showers generate disk-like ionization fronts propagating with a relativistic velocity and creating fast decaying plasma. We study the reflection of a radio wave, such as the one from a radar transmitter or commercial radio and TV station, from the relativistic ionization front. The reflected wave will be frequency upshifted due to the relativistic Doppler effect and propagate almost normally to the front due to relativistic aberration. The amplitude of the reflected wave depends strongly on the front velocity and parameters (density, collision frequency) of the plasma behind the front. We develop a theory that allows one to find the reflected wave. Using this theory and typical parameters of extensive air showers, we discuss the feasibility of UHECR detection.

Relativistic Ionization Fronts

We derive the equations for the propagation of relativistic ionization fronts in both static and moving gases. We focus on the supersonic R-type phase that occurs right after a source turns on, and we compare the nonrelativistic and relativistic solutions for several important cases. Relativistic corrections can be significant up until the light-crossing time of the equilibrium Stromgren sphere. For a static medium, we obtain exact analytical solutions and apply them to the illustrative problems of an O star in a molecular cloud and a starburst in a high-redshift cosmological halo. Relativistic corrections can be important at early times when the H II regions are small, as well as at later times, if a density gradient causes the I-front to accelerate. For the cosmologically-expanding IGM, we derive an analytical solution in the case of a steady source and a constant clumping factor. Here relativistic corrections are significant for short-lived, highly-luminous sources like QSOs at the end of reionization, but negligible for weaker or higher-redshift sources. Finally, we numerically calculate the evolution of relativistic I-fronts in the presence of small-scale structure and infall, for a large galaxy undergoing a starburst and a luminous, high-redshift QSO. For such strong and short-lived sources, the relativistic corrections are quite significant, and small-scale structure can decrease the size of the H II region by up to an additional ~25%. (abridged)

Interaction of Oblique Incident Electromagnetic Wave with Relativistic Ionization Front

Interactions of oblique incident probe wave with oncoming ionization fronts have been investigated using moving boundary conditions. Field conversion coefficients of reflection, transmission and magnetic modes produced in the interactions are derived. Phase matching conditions at the front and frequency up-shifting formulas for the three modes are also presented.

Frequency conversion of probe wave produced by 2D interaction with relativistic ionization front

Frequency conversion of probe electromagnetic wave induced by relativistic ionization front is theoretically analysed based on ray-tracing equations in different regimes. Downshifting as well as upshifting in frequency produced by the front is predicted. The reflected and transmitted angles can be also dramatically changed in certain cases.

Photon acceleration of ultrashort laser pulses by relativistic ionization fronts.

We present experimental results from the collision of weak ultrashort pulses with relativistic ionization fronts in copropagation and counterpropagation. The observed frequency upshifts of the probe pulses provide not only information about the electron density of the ionization front but also reveal the fine structure of the front. The connection between the correlation lengths for copropagation and counterpropagation and the longitudinal and transverse dimensions of the ionization front is also demonstrated thus showing the feasibility of using the frequency upshift experienced by short probe pulses to fully characterize relativistic ionization fronts and other relativistic coherent structures in laser-produced plasmas.

Two-dimensional collision of probe photons with relativistic ionization fronts.

The collision of a probe laser pulse with a relativistic ionization front is analyzed via two-dimensional ray-tracing theory and simulations. It is shown that collisions in higher dimensions lead to new regimes for the frequency upshift of the probe photons; the frequency upshift can be considerably higher for particular collision angles that maximize the interaction length with the ionization front gradient. Finite ionization fronts also lead to angle-dependent frequency upshifts, thus acting as diffraction gratings.

Experimental observation of further frequency upshift from dc to ac radiation converter with perpendicular dc magnetic field

A frequency upshift of a short microwave pulse is generated by the interaction between a relativistic underdense ionization front and a periodic electrostatic field with a perpendicular dc magnetic field. When the dc magnetic field is applied, further frequency upshift of 3 GHz is observed with respect to an unmagnetized case which has typically a GHz range. The radiation frequency depends on both the plasma density and the strength of the dc magnetic field, i.e., the plasma frequency and the cyclotron frequency. The frequency of the emitted radiation is in reasonable agreement with the theoretical values.

“Single-cycle” ionization effects in laser–matter interaction

We investigate numerical effects related to “single-cycle” ionization of dense matter by an ultra-short laser pulse. The strongly nonadiabatic response of electrons leads to generation of a MG steady magnetic field in laser–solid interaction. By using two-beam interference, it is possible to create periodic density structures able to trap light and to generate relativistic ionization fronts.