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Journals >Matter and Radiation at Extremes >Volume 8 >Issue 6 >Page 064005 > Article

Matter and Radiation at Extremes
Vol. 8, Issue 6, 064005 (2023)

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

Zheng Gong¹, Michael J. Quin¹, Simon Bohlen², Christoph H. Keitel¹..., Kristjan Põder² and Matteo Tamburini¹|Show fewer author(s)

Author Affiliations

¹Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany

²Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany

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DOI: 10.1063/5.0152382 Cite this Article

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

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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.

\frac{d p_{y}}{d ϕ} = \frac{| e |}{c} \frac{d}{d ϕ} (A_{0, y} + A_{1, y}),

(1)

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\frac{d p_{x}}{d ϕ} = - \frac{| e |}{ω_{0}} \frac{p_{y}}{p_{-}} (B_{0, z} + B_{1, z}),

(2)

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\begin{align} \frac{d p_{x}}{d ϕ} & = \frac{m_{e}^{2} c^{2}}{p_{-}} [a_{0}^{2} \cos ϕ \sin ϕ + a_{0} a_{1} \sin (2 k_{0} x + ϕ_{1}) \\ - a_{1}^{2} \cos (ϕ + 2 k_{0} x + ϕ_{1}) \sin (ϕ + 2 k_{0} x + ϕ_{1})] . \end{align}

(3)

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\frac{| e | E_{y, 0}}{m_{e} ω_{0} c} = a_{0} \exp \{- {(\frac{ϕ - ϕ_{0}}{ω_{0} τ_{0} / \sqrt{2 \ln 2}})}^{2}\} \cos ϕ,

(4)

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\frac{| e | E_{y, 1}}{m_{e} ω_{0} c} = a_{1} \exp \{- {(\frac{ϕ + 2 k_{0} x - ϕ_{1}}{ω_{0} τ_{0} / \sqrt{2 \ln 2}})}^{2}\} \cos (ϕ + 2 k_{0} x),

(5)

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\frac{d p_{x}}{d t} = - | e | E_{x} (ξ),

(6)

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\frac{d ξ}{d t} = \frac{p_{x}}{m_{e} \sqrt{1 + {(p_{x} / m_{e} c)}^{2}}} - v_{d},

(7)

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H (ξ, p_{x}) = - | e | φ (ξ) + c \sqrt{m_{e}^{2} c^{2} + p_{x}^{2}} - v_{d} p_{x} .

(8)

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E_{x} (ξ) = \{\begin{cases} 0 & if ξ ⩽ ξ_{4}, \\ - E_{0} \frac{ξ - ξ_{4}}{ξ_{3} - ξ_{4}} & if ξ_{4} < ξ ⩽ ξ_{3}, \\ - E_{0} \frac{ξ_{0} - ξ}{ξ_{0} - ξ_{3}} & if ξ_{3} < ξ ⩽ ξ_{0}, \\ E_{0} \frac{ξ - ξ_{0}}{ξ_{1} - ξ_{0}} & if ξ_{0} < ξ ⩽ ξ_{1}, \\ E_{0} \frac{ξ_{2} - ξ}{ξ_{2} - ξ_{1}} & if ξ_{1} < ξ ⩽ ξ_{2}, \\ 0 & if ξ_{2} < ξ, \end{cases}

(9)

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φ (ξ) = \{\begin{cases} 0 & if ξ ⩽ ξ_{4}, \\ E_{0} \frac{{(ξ - ξ_{4})}^{2}}{2 (ξ_{3} - ξ_{4})} & if ξ_{4} < ξ ⩽ ξ_{3}, \\ E_{0} \frac{ξ_{0} - ξ_{4}}{2} - E_{0} \frac{{(ξ_{0} - ξ)}^{2}}{2 (ξ_{0} - ξ_{3})} & if ξ_{3} < ξ ⩽ ξ_{0}, \\ E_{0} \frac{ξ_{2} - ξ_{0}}{2} - E_{0} \frac{{(ξ - ξ_{0})}^{2}}{2 (ξ_{1} - ξ_{0})} & if ξ_{0} < ξ ⩽ ξ_{1}, \\ E_{0} \frac{{(ξ - ξ_{2})}^{2}}{2 (ξ_{2} - ξ_{1})} & if ξ_{1} < ξ ⩽ ξ_{2}, \\ 0 & if ξ_{2} < ξ . \end{cases}

(10)

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(1 - β_{d}^{2}) {(\frac{p_{th}}{m_{e} c})}^{2} - 2 β_{d} A (\frac{p_{th}}{m_{e} c}) + 1 - A^{2} = 0,

(11)

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\frac{p_{th}^{\pm}}{m_{e} c} = \frac{β_{d} A \pm \sqrt{β_{d}^{2} + A^{2} - 1}}{1 - β_{d}^{2}} .

(12)

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\frac{p_{th}^{-}}{m_{e} c} \approx \frac{\sqrt{1 - S} (ρ \tilde{φ} + \sqrt{S}) - \sqrt{ρ^{2} {\tilde{φ}}^{2} + 2 ρ \tilde{φ} \sqrt{S}}}{S} .

(13)

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a_{1}^{*} = {[\frac{\sqrt{1 - S} (ρ \tilde{φ} + \sqrt{S}) - \sqrt{ρ^{2} {\tilde{φ}}^{2} + 2 ρ \tilde{φ} \sqrt{S}}}{κ_{p} a_{0}^{n_{0}} S}]}^{1 / n_{1}} .

(14)

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

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