Generating ultradense pair beams using 400 $\mathrm{GeV}/c$ protons

An experimental scheme is presented for generating low-divergence, ultradense, relativistic, electron-positron beams using 400 $\mathrm{GeV}/c$ protons available at facilities such as HiRadMat and AWAKE at CERN. Preliminary Monte Carlo and particle-in-cell simulations demonstrate the possibility of generating beams containing ${10}^{13}–{10}^{14}$ electron-positron pairs at sufficiently high densities to drive collisionless beam-plasma instabilities, which are expected to play an important role in magnetic field generation and the related radiation signatures of relativistic astrophysical phenomena. The pair beams are quasineutral, with size exceeding several skin depths in all dimensions, allowing the examination of the effect of competition between transverse and longitudinal instability modes on the growth of magnetic fields. Furthermore, the presented scheme allows for the possibility of controlling the relative density of hadrons to electron-positron pairs in the beam, making it possible to explore the parameter spaces for different astrophysical environments.

Figure 1

Proposed experimental setup. Beams composed of electrons, positrons, photons, protons, and other hadrons are generated using a beryllium target followed by a lead converter. The beam-plasma interaction can be studied by driving the beam into a plasma cell. For this plasma cell, an inductively coupled discharge is proposed in Sec. 5. Since the bulk of the electrons and positrons in the beam have much smaller momentum than the hadrons, dipole magnets can be used to deflect $e^{+}{e}^{-}$ out of the beam to study their energy spectra, while the hadrons are deflected less and are absorbed by the beam dump.

Figure 2

The dependencies of peak densities of each beam species on Be target and Pb converter thicknesses is shown for four configurations. (a) and (b) show the densities obtained for single-component targets of beryllium and lead, while (c) and (d) show the sensitivities of particle densities to a change in thickness of beryllium or lead from a configuration that generates a high density of $e^{+}{e}^{-}$ pairs (that is, 30-cm beryllium target with a 4-cm lead converter). The largest pair beam densities are only achieved by using a configuration that contains both beryllium and lead, and the thickness of lead can be modified to alter the ratio of $e^{+}{e}^{-}$ to hadrons in the beam. Densities are obtained assuming an incident $p^{+}$ beam with radius $\sigma =$ 0.5 mm and are presented in units per incident proton, so that the numbers can be scaled to the bunch intensity of the proton facility. A pulse duration of 375 ps is assumed to obtain the peak density from the simulated peak fluence.

Figure 3

Energy spectra (left) and angle-position phase space plots (right) obtained in the case of a 30-cm beryllium target and 4-cm lead converter. The simulation setup is the same as the one mentioned in Table 2. The energy spectra are displayed in the ranges where their spectra are most significant, while insets display the spectra extending to much higher energies. In the angle-position phase space plots, x refers to the position along the in-plane transverse direction, and $z$ is the longitudinal direction. ${\theta }_{\mathbf{x}}$ is the angle $\arctan (v_x$/$v_z$), where $v_x$ and $v_z$ are the components of the particle velocity along the $x$ and $z$ axes (measured in the laboratory frame). The plots are normalized and displayed with a color mapping that clearly depicts the half maxima.

Figure 4

Simulation results of the interaction between an electron-positron-proton bunch and a static plasma with density ${10}^{14}{\mathrm{cm}}^{-3}$ at a time $t=705[1/{\omega }_{\mathrm{p}}]=1.27\mathrm{ns}$. (a) Density filaments of electrons (blue) and protons (orange). (b) Transverse magnetic field $B_{\perp }$ filaments due to current filamentation. (c) Longitudinal electric fields $E_{\parallel }$ and (d) transverse electric fields $E_{\perp }$ attributed to charge separation and inductive effects. Units are such that one plasma period $[1/{\omega }_{\mathrm{p}}]$ corresponds to $[1/{\omega }_{\mathrm{p}}]=1.8\mathrm{ps}$, while one skin depth $[c/{\omega }_{\mathrm{p}}]$ corresponds to $[c/{\omega }_{\mathrm{p}}]=530\mu \mathrm{m}$, and magnetic and electric field units are $[m_{\mathrm{e}}{\omega }_{\mathrm{p}}c/e]=3.2\mathrm{T}$ and $[m_{\mathrm{e}}{\omega }_{\mathrm{p}}c/e]=\mathrm{GV}/\mathrm{m}$, respectively.

Figure 5

Evolution of energies contained within transverse magnetic field ${\epsilon }_{B\perp }$ (red, lower curve), transverse electric field ${\epsilon }_{E\perp }$ (green, middle curve), and longitudinal electric field ${\epsilon }_{E\parallel }$ (blue, upper curve) as the beam propagates, normalized to the initial kinetic energy of the beam ${\epsilon }_{\mathrm{p}}=2n_{\mathrm{b}}V{m}_{\mathrm{e}}{c}^2({\gamma }_{\mathrm{b}}-1)$, where $V$ is the volume of the beam and $2n_{\mathrm{b}}$ is the combined density of the $e^{-}$ and $e^{+}$ in the beam.

Figure 6

The design for a cylindrical inductive discharge composed of coils wrapped around sections of glass tube. The glass tubes are separated by port crosses where diagnostics can be inserted. The coils are connected to a radiofrequency power source via an impedance matching network that ensures maximum coupling of electrical power into the plasma. The generated plasma is expected to extend between the coils, which means they can be spaced apart.