Spin-polarized electron beam generation in the colliding-pulse injection scheme

Gong Zheng; Quin Michael J.; Bohlen Simon; Keitel Christoph H.; Põder Kristjan; Tamburini Matteo

doi:10.1063/5.0152382

Volume 8 Issue 6

Nov. 2023

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Gong Zheng, Quin Michael J., Bohlen Simon, Keitel Christoph H., Põder Kristjan, Tamburini Matteo. Spin-polarized electron beam generation in the colliding-pulse injection scheme[J]. Matter and Radiation at Extremes, 2023, 8(6): 064005. doi: 10.1063/5.0152382

Citation:

Gong Zheng, Quin Michael J., Bohlen Simon, Keitel Christoph H., Põder Kristjan, Tamburini Matteo. Spin-polarized electron beam generation in the colliding-pulse injection scheme[J]. Matter and Radiation at Extremes, 2023, 8(6): 064005. doi: 10.1063/5.0152382

Citation:

Gong Zheng, Quin Michael J., Bohlen Simon, Keitel Christoph H., Põder Kristjan, Tamburini Matteo. Spin-polarized electron beam generation in the colliding-pulse injection scheme[J]. Matter and Radiation at Extremes, 2023, 8(6): 064005. doi: 10.1063/5.0152382

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Spin-polarized electron beam generation in the colliding-pulse injection scheme

doi: 10.1063/5.0152382

1.
Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
2.
Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany

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Corresponding author: a)Author to whom correspondence should be addressed: gong@mpi-hd.mpg.de
Received Date: 2023-03-29
Accepted Date: 2023-08-22

Available Online: 2023-11-01

Publish Date: 2023-11-01

Abstract

Abstract

Employing colliding-pulse injection has been shown to enable the generation of high-quality electron beams from laser–plasma accelerators. Here, by using test particle simulations, Hamiltonian analysis, and multidimensional particle-in-cell simulations, we lay the theoretical framework for spin-polarized electron beam generation in the colliding-pulse injection scheme. Furthermore, we show that this scheme enables the production of quasi-monoenergetic electron beams in excess of 80% polarization and tens of pC charge with commercial 10-TW-class laser systems.

The authors have no conflicts to disclose.
Conflict of Interest
Z.G. carried out the simulations by using FBPIC with the spin dynamics model implemented by M.J.Q. Z.G.performed the analysis with assistance from M.T.. The manuscript was written by Z.G. and M.T, with feedback from S.B. C.H.K. and K.P. M.T. supervised the project. All authors discussed the results presented in the paper.
Author Contributions
Zheng Gong: Conceptualization (equal); Data curation (lead); Formal analysis (equal); Investigation (equal); Methodology (lead); Visualization (lead); Writing – original draft (equal); Writing – review & editing (equal). Michael J. Quin: Investigation (supporting); Software (lead); Writing – review & editing (equal). Simon Bohlen: Investigation (supporting); Writing – review & editing (equal). Christoph H. Keitel: Resources (equal); Writing – review & editing (equal). Kristjan Põder: Conceptualization (supporting); Funding acquisition (supporting); Investigation (supporting); Project administration (supporting); Resources (equal); Supervision (supporting); Writing – review & editing (equal). Matteo Tamburini: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Project administration (lead); Resources (equal); Supervision (lead); Writing – original draft (equal); Writing – review & editing (equal).
The data that support the findings of this study are available from the corresponding author upon reasonable request.
The spin of an electron in electric E and magnetic B fields precesses according to the Thomas–Bargmann–Michel–Telegdi (TBMT) equation⁷¹,⁷²dsdt=Ω×s,where Ω = Ω_T + Ω_a, withΩT=|e|mecBγ−β1+γ×E,Ωa=ae|e|mecB−γ1+γβ(β⋅B)−β×E.Here, γ=1+p2/me2c2 is the Lorentz factor of the electron, β = p/γm_ec is its normalized velocity, and a_e ≈ 1.16 × 10⁻³ is the electron anomalous magnetic moment. Note that Eqs. (A1)–(A3) are specific to electrons through their dependence on the anomalous magnetic moment a_e. The leapfrog equation obtained by discretizing Eq. (A1) and with electromagnetic fields Eⁿ and Bⁿ at step n issn+1/2−sn−1/2Δt=Ωn×sn.Here, we have used the following definitions of the midpoint spin and momentum:sn=sn+1/2+sn−1/22,pn=pn+1/2+pn−1/22,γn=1+(pn)2/me2c2.By inserting these quantities into Eq. (A4), one immediately obtains |s^n+1/2| = |s^n−1/2|. Equation (A4) can be rewritten assn+1/2=s′+(h×sn+1/2),where h = ΩⁿΔt/2 and s′ = s^n−1/2 + h × s^n−1/2. Now, Eq. (A8) is a linear system of equations in the unknown s^n+1/2, whose solution issn+1/2=o[s′+(h⋅s′)h+h×s′],where o = 1/(1 + h²). The same approach discussed above can be employed for advancing the momentum.⁹⁴
Following the work described in Refs. 36 and 42, several schemes utilizing pre-polarized plasma generation via laser-induced molecular photodissociation³⁷–³⁹ have been proposed.⁴³–⁵⁵ Although not used in the present article, we have implemented in FBPIC not only the electron spin degrees of freedom and their evolution as detailed above, but also the capability to approximately model the initial spin state of electrons ionized from the photodissociation products of hydrogen halide molecules such as HCl. In fact, as with the momentum and position, an initial value for the spin must be provided for all species of particles.
For molecules such as HCl, which are not considered in this paper, the unpaired outer-shell electron of H and Cl has an initial spin along the propagation axis of the dissociation laser after ionization, whereas the many spin-paired inner-shell electrons must be treated differently. In practice, when an inner-shell electron of Cl is ionized, its initial spin is randomly oriented in space, to account of the fact that no orientation is present for these electrons. Ideally, a more sophisticated model would include quantum mechanical effects when determining the initial spin of each successive electron emitted by ionization, but our simpler approach suffices for capturing the essential dynamics of polarized electrons obtained with the technique of laser-induced molecular photodissociation.

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