Suppression of pair beam instabilities in a laboratory analogue of blazar pair cascades

TL;DR

This study addresses whether electromagnetic beam-plasma instabilities could dissipate energy from TeV blazar–induced pair cascades during their propagation through cosmic voids. Using a laboratory analogue, the authors generate dense electron–positron pair beams with ultra-relativistic protons and study their propagation through a metre-scale ambient plasma, employing FLUKA simulations, 3D PIC simulations, and a suite of precise diagnostics including a time-resolved Faraday rotation probe. They find that non-ideal beam properties, such as finite angular spread and energy dispersion, suppress the fastest-growing instabilities, with an experimental growth-rate bound of $\langle \Gamma_{\mathrm{exp}}\rangle \le 0.7\ \mathrm{ns^{-1}}$ and a maximum magnetic field of $B_{\max}\approx 7\ \mathrm{mT}$ in PIC, far below the predictions for idealized beams. Together with scaling analyses of the Vlasov-Landau-Maxwell equations, these results indicate that beam-plasma instabilities are strongly suppressed for realistic blazar-jet conditions, leaving the intergalactic magnetic-field inferences from $\gamma$-ray observations robust. The work provides a concrete laboratory validation that the lack of GeV cascade emission from TeV blazars is unlikely to be explained by such instabilities, supporting the hypothesis that a relic, yet-unmeasured IGMF governs the cascade signatures.

Abstract

The generation of dense electron-positron pair beams in the laboratory can enable direct tests of theoretical models of $γ$-ray bursts and active galactic nuclei. We have successfully achieved this using ultra-relativistic protons accelerated by the Super Proton Synchrotron at CERN. In the first application of this experimental platform, the stability of the pair beam is studied as it propagates through a metre-length plasma, analogous to TeV $γ$-ray induced pair cascades in the intergalactic medium. It has been argued that pair beam instabilities disrupt the cascade, thus accounting for the observed lack of reprocessed GeV emission from TeV blazars. If true this would remove the need for a moderate strength intergalactic magnetic field to explain the observations. We find that the pair beam instability is suppressed if the beam is not perfectly collimated or monochromatic, hence the lower limit to the intergalactic magnetic field inferred from $γ$-ray observations of blazars is robust.

Figures (18)

• Figure 1: Experimental setup. (a) Protons with 440GeV/$c$ momentum are extracted from the SPS accelerator with temporal profile measured using an integrating current transformer (inset). The protons irradiate a solid target (360mm graphite plus 10mm tantalum) with a maximum fluence exceeding $3\times10^{11}$ protons in a single bunch of duration 0.25ns (1-$\sigma$) and transverse size $\sigma_r = 1mm$. A secondary beam is generated via hadronic and electromagnetic cascades, containing a dominating fluence of electron-positron pairs ($N_{\mathrm{e}^{\pm}}>10^{13}$), plus hadrons, $\gamma$-rays and other secondaries. (b) Measurements of the transverse beam profile using $70$ mm $\times\, 50$ mm $\times \, 0.25$ mm chromium-doped ceramic (Chromox) luminescence screens, viewed by a digital camera at a standoff distance of $3.8m$. The spatial resolution is limited to $100µm$ by the Chromox transluscence. (c) Downstream of the target, the beam passes though a metre-length argon plasma produced by an inductively-coupled radio-frequency discharge. The longitudinal plasma density profile is measured using a Langmuir probe and confirmed during the experiment using optical emission spectroscopy. Pair beam filamentation due to beam-plasma instability is measured using a luminescence screen placed downstream of the plasma (camera positioned at a standoff distance 3.9m), and a Faraday rotation diagnostic measures the growth of magnetic fields inside the plasma. (d) The electron and positron energy spectra are measured using a magnetic particle spectrometer arrowsmith2023laboratory, shown here re-scaled according to the size of the collecting aperture to compare directly with FLUKA simulations of the spectra inside the plasma.
• Figure 1: Simplified geometry of the experiment simulated using FLUKA. The plasma discharge vessel is modelled as a stainless steel tube with two glass sections where the inductive coils are located. The surrounding experimental area including the downstream beam dump as well as the concrete walls and shielding are also included in FLUKA simulations (not shown). The exact material compositions are used in all cases.
• Figure 2: Magnetic field and beam profile measurements. (a) Magnetic fields are measured at the end of the plasma using a time-resolved Faraday rotation technique. A linearly polarized laser beam ($\lambda=532nm$) is passed twice through a magneto-optic crystal (TGG, 12mm length, 2mm diameter), suspended in the plasma by a ceramic re-entrant tube (orientation shown in the inset), before passing through a second polarizing filter offset by $45°$ from the initial polarization. The change in laser intensity measured by a fast photodiode ($\Delta V = V-V_0/2$) is plotted as a function of time, with the pair beam expected to pass the probe $2.7ns$ after the beam enters the plasma (the signal is shown a few ns before and afterwards to account for the uncertainty in the exact timing). The mean signal from five shots is plotted, with corresponding standard deviation represented by the red shaded region. The blue shaded regions show the standard deviation of the intrinsic electronic noise. (b) The transverse beam profile is measured using a Chromox luminescence screen positioned $90mm$ downstream of the plasma discharge. The residual primary proton beam is subtracted from the images (see Methods), leaving the fluence of electron-positron pairs (plus additional secondaries). The radial lineouts are shown when the plasma is present ($p_{\mathrm{g}} = 4Pa$, $P_{\mathrm{abs}}=240\pm10W$) and when there is no plasma ($p_{\mathrm{g}} = 0.5Pa$, $P_{\mathrm{abs}}=0W$), with the image data shown in the inset. The shaded regions represent the standard deviation of the lineout pixel counts combined with the uncertainty in the absolute calibration.
• Figure 2: Obtaining the azimuthal magnetic field at the Faraday probe position in the absence of plasma using FLUKA simulations. (a) The particle fluence is plotted as a function of radius at the position corresponding to the Faraday probe inside the plasma vessel (obtained from a FLUKA simulation) for electrons (blue), positrons (red), protons (green), positive pions (orange) and negative pions (purple). (b) Ampère's circuital law is used to calculate the corresponding azimuthally-oriented magnetic field as a function of radius.
• Figure 3: Three-dimensional particle-in-cell simulations. 3D simulations of the beam-plasma interaction are performed using the particle-in-cell code OSIRIS fonseca2002osiris for two cases: (a) with conditions closely resembling the experimental beam and ambient plasma (labelled 'experimental'), and (b) an idealized case with a collimated, monoenergetic ($\gamma_{\pm}=10^3$) pairs (labelled 'idealized'). In (a) and (b), the left panels show a central slice of the electron and positron densities in the longitudinal plane ($y$-$z$) at the time when the beam passes the Faraday probe ($t=2.7ns$ after entering the plasma), whilst the right panels show a central slice of the transverse plane ($x$-$y$) when the beam passes the downstream luminescence screen ($t=3.4ns$). (c) The peak magnetic field is plotted as a function of propagation distance through the plasma, with the background shading showing the ambient plasma density. The maximum growth rate of the peak magnetic field is obtained by the shown fits (red-dashed). The anti-correlation of magnetic field and plasma density is an effect of the varying level of return current.