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Journals >Matter and Radiation at Extremes >Volume 8 >Issue 5 >Page 054003 > Article

Matter and Radiation at Extremes
Vol. 8, Issue 5, 054003 (2023)

Quantum splitting of electron peaks in ultra-strong fields

Bo Zhang, Zhi-Meng Zhang, and Wei-Min Zhou

Author Affiliations

Key Laboratory of Plasma Physics, Research Center of Laser Fusion, CAEP, Mianshan Rd 64, 621900 Mianyang, Sichuan, China

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DOI: 10.1063/5.0157663 Cite this Article

Bo Zhang, Zhi-Meng Zhang, Wei-Min Zhou. Quantum splitting of electron peaks in ultra-strong fields[J]. Matter and Radiation at Extremes, 2023, 8(5): 054003 Copy Citation Text

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Abstract

Effects of multiple nonlinear Compton scattering on electrons in ultra-strong fields are described using analytic formulas similar to those in the theory of multiple bremsstrahlung. Based on these analytic formulas, a new pure quantum effect of multiple nonlinear Compton scattering called quantum peak splitting is identified: the electron peak splits into two when the average number of nonlinear Compton scatterings per electron passes a threshold of 5.1 and is below 9. Quantum peak splitting stems from the discreteness of quantum radiation reaction, with one of the split peaks being formed by electrons emitting zero to three times and the other by electrons emitting four or more times. This effect provides a new mechanism for the formation of electron peaks, imposes a new beamstrahlung limit on future colliders, and corrects the picture of quantum radiation reaction. Experiments can be performed on lasers with intensities ≳10²¹ W/cm², which are reachable on PW-scale facilities.

\begin{align} \frac{d W_{NCS}}{d δ d t} & = \frac{α}{π \sqrt{3}} \frac{m^{2}}{p_{0}} [(1 - δ + \frac{1}{1 - δ}) K_{2 / 3} (\frac{2 δ}{3 χ (1 - δ)}) \\ - \int_{2 δ / 3 χ (1 - δ)}^{\infty} d y K_{1 / 3} (y)], δ \in (0, 1), \end{align}

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\begin{align} \frac{d W_{QSR}}{d t d δ} & = \frac{\sqrt{3} α}{2 π} \frac{m_{q} χ_{q}}{γ} \frac{1 - δ}{δ} \\ \times [κ (y) + y^{3} {(\frac{3 χ_{q}}{2})}^{2} (1 - δ) K_{2 / 3} (y)], \end{align}

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κ (y) = y \int_{y}^{\infty} K_{5 / 3} (x) d x,

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y = \frac{2 δ}{3 χ_{q} (1 - δ)} .

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\frac{d W}{d δ d t} \propto δ^{- 2 / 3} e^{- δ / δ_{0}}

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f_{in} (δ) \approx A \frac{α m^{2}}{p_{0}} {(\frac{χ}{δ})}^{2 / 3} \exp (- \frac{δ}{χ})

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F (x) = P_{0} f_{0} (x) + \sum_{i = 1}^{\infty} P_{i} f_{i} (x),

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\frac{d W_{NCS}}{d t} = \int_{0}^{1} d δ \frac{d W}{d δ d t} \approx \frac{1.44 α χ m}{γ ℏ} \approx 0.01 (1 - \cos θ) a_{0} ω_{0},

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\frac{d W_{QSR}}{d t} \approx \frac{5 α B m}{2 \sqrt{3} B_{q} ℏ},

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P_{i} (r) \approx \frac{r^{i}}{i!} e^{- r} (i \geq 0) .

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f_{i} (η) \approx \int d η^{'} f_{i - 1} (η^{'}) \bar{R} (η^{'} - η) (i \geq 1),

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\bar{R} (δ) = \frac{\int d t \frac{d W}{d δ d t}}{\int d δ \int d t \frac{d W}{d δ d t}}

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R (δ) \approx R^{A} (δ) = \frac{χ^{- 1 / 3} δ^{- 2 / 3}}{Γ (1 / 3)} e^{- δ / χ} .

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f_{i, χ} (η) \approx f_{i, χ}^{A} (η) = \frac{χ^{- i / 3}}{Γ (i / 3)} {(1 - η)}^{i / 3 - 1} e^{- (1 - η) / χ}

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\partial_{η} F (η) \approx - χ \sum_{i = 1}^{\infty} \frac{r^{i} [(i / 3 - 1) ξ^{i / 3 - 2} - ξ^{i / 3 - 1}]}{i! Γ (i / 3)} e^{- r} e^{- ξ},

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Δ η_{peak} \approx \frac{χ}{3} (r - 3.5) .

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\begin{align} F (η_{cm}) & \approx \sum_{i, i^{'} = 0}^{\infty} P_{i} (n_{γ, e^{-}}) P_{i^{'}} (n_{γ, e^{+}}) \\ \times \int_{η_{cm}}^{1} d η_{cm}^{'} f_{i, χ / 2}^{A} (η_{cm}^{'}) f_{i^{'}, χ / 2}^{A} (1 - η_{cm}^{'} + η_{cm}), \end{align}

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f_{i, χ}^{A} (η) \approx \int_{η}^{1} d η^{'} f_{i^{'}, χ}^{A} (η) f_{i - i^{'}, χ}^{A} (1 + η - η^{'})

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P_{k} (n_{γ, e^{-}} + n_{γ, e^{+}}) = \sum_{k^{'} = 0}^{k} P_{k^{'}} (n_{γ, e^{-}}) P_{k - k^{'}} (n_{γ, e^{+}}),

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F (η_{cm}) \approx \sum_{k = 0}^{\infty} P_{k} (2 n_{γ}) f_{i, χ / 2}^{A} (η_{cm}) .

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Bo Zhang, Zhi-Meng Zhang, Wei-Min Zhou. Quantum splitting of electron peaks in ultra-strong fields[J]. Matter and Radiation at Extremes, 2023, 8(5): 054003

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