Electron beam guiding by a laser Bessel beam

Open Access

Electron beam guiding by a laser Bessel beam

Levi Schächter and W. D. Kimura

Phys. Rev. Accel. Beams 23, 081301 – Published 3 August 2020

Abstract

We investigate the dynamics of electrons counterpropagating along a radially polarized optical Bessel beam (OBB). (i) It is shown that a significant fraction of the electrons can be transversally trapped by the OBB even in the case of “unmatched” injection. Moreover, (ii) these transversally trapped particles (TTPs) can be transported without loss along many thousands of wavelengths. As long as there is full longitudinal overlap between the electrons and laser pulse, this transport distance is limited only by the length of the OBB region. (iii) The unique profile of the transverse field components facilitates guiding either azimuthally symmetric pencil beams or annular beams. Space charge tends to totally suppress the annular beams, and it reduces the amount of charge trapped on axis for pencil beams. (iv) Assessment of the emittance of the TTPs alone reveals typical values of 10–50 pm. In fact, our simulations indicate if we trace the emittance of those particles that are trapped from the input to the output of the OBB, we find that this emittance is conserved. (v) We developed an analytic model whereby we average over the fast oscillation associated with the counterpropagating electrons and OBB. The resulting Hamiltonian has a Bessel potential $J_{1}^{2} (u)$ , which, when operated in the linear regime near equilibrium, causes rotation of the phase space. A Kapchinskij-Vladimirskij beam-envelope equation is derived including space-charge and emittance effects. Relying on conservation of the longitudinal canonical momentum, the energy spread in the interaction region is determined in terms of the OBB intensity and the electron energy.

Received 7 April 2020
Accepted 15 June 2020

DOI:https://doi.org/10.1103/PhysRevAccelBeams.23.081301

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Beam optics

Accelerators & Beams

Authors & Affiliations

Levi Schächter ^1,* and W. D. Kimura ²

¹Technion–Israel Institute of Technology, Haifa 32000, Israel
²STI Optronics, Inc., Bellevue, Washington 98005, USA

^*Corresponding author. levis@technion.ac.il

Article Text

Click to Expand

References

Click to Expand

Issue

Vol. 23, Iss. 8 — August 2020

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
An axicon lens converts a radially polarized annular $(R_{int} < r < R_{ext})$ laser beam to an OBB on axis. The electrons counterpropagate against the Bessel beam. The laser beam propagates at an angle $θ_{0}$ relative to the axis; the radial electric field before the axicon lens is $E_{r, 0}$ , which translates on axis after the axicon to an amplitude $E_{z, 0} \equiv E_{0} = E_{r, 0} \sin θ_{0}$ . Not to scale.
Reuse & Permissions
Figure 2
Phase space in the space-charge-free case. The trapping of particles in the vicinity of the equilibrium points is evident: $| {\bar{x}}_{eq} | \sim 0$ and $| {\bar{x}}_{eq} | \sim 3.512$ . The initial beam’s phase space does not cover the third equilibrium $(| {\bar{x}}_{eq} | \sim 6.43)$ since $| \bar{x} | < 5$ ; therefore, electrons are not trapped in this state. (a) At $z = L / 2$ . (b) At $z = L$ .
Reuse & Permissions
Figure 3
(a) $κ_{SC} = 4.2 \times 10^{- 6}$ , $z = L / 2$ . (c) $κ_{SC} = 4.2 \times 10^{- 6}$ , $z = L$ . Space charge tends to reduce the trapping when comparing $κ_{sc} = 4.2 \times 10^{- 6}$ with the zero space-charge case $κ_{sc} = 0$ as revealed in Fig. 2. (b) $κ_{SC} = 4.2 \times 10^{- 5}$ , $z = L / 2$ . (d) $κ_{SC} = 4.2 \times 10^{- 5}$ , $z = L$ . Elevating the charge by one order of magnitude suppresses entirely the annular beam.
Reuse & Permissions
Figure 4
Guiding of a pencil beam of electrons by OBB. (a) $κ_{SC} = 4.2 \times 10^{- 6}$ , $z = L / 2$ , $p_{x, \max} = 10^{- 4}$ . (c) $κ_{SC} = 4.2 \times 10^{- 6}$ , $z = L$ , $p_{x, \max} = 10^{- 4}$ . The low space-charge ( $κ_{sc} = 4.2 \times 10^{- 6}$ ) beam is significantly squeezed spatially, but the spread of the transverse momentum increases by almost one order of magnitude. The initial emittance is 0.1 nm. (e) Phase space at the input is marked with red, whereas in green are labeled particles at the input that eventually become trapped and make it to the output. A well-defined region $(| {\bar{x}}_{i} | \leq 1)$ in the phase space is occupied by only those electrons that will become trapped, implying that the emittance of the trapped electrons is within a good approximation constant. (b),(d),(f) The same parameters as (a),(c),(e) except ${\bar{x}}_{\max} = 1.0$ , ${\bar{p}}_{x, \max} = 4 \times 10^{- 4}$ . Note that many fewer electrons are trapped, since the selection is more stringent, but the emittance of the trapped particles (0.2 nm) is significantly lower than that of the entire ensemble at the input (1 nm).
Reuse & Permissions
Figure 5
Dispersion curves corresponding to solution of Eq. (c2). (a) In red is the first passband and in blue its polynomial approximation. (b) The second passband is relatively far away from the first one, and it is one order of magnitude narrower. The eigenvalues are independent of the angle $χ_{0}$ .
Reuse & Permissions

Physical Review Accelerators and Beams