This paper explores direct density modulation of high-current electron beam emission from an RF cold cathode using optical excitation. We theoretically study the photo-assisted field emission of periodically bunched electron beams of various pulse shapes under the combined excitation of an RF field and an optical field, using an exact quantum model. Both continuous-wave (CW) and pulsed optical fields are considered. The emission current pulse amplitude, pulse width, electron number density per pulse, as well as pulse shape and its harmonic contents are investigated in detail. For CW photon sources in the UV to NIR range (i.e., 200–1200 nm), increasing the optical intensity under an RF bias tends to change the current pulse from a Gaussian to sinusoidal-like shape, thus offering strong flexibility to control the frequency components in beam current emission. Pulsed photon sources combined with an RF field can produce sharp, high-current electron bunches with pulse duration comparable with or even less than that of the optical pulse. A contour map of the density modulation depth is constructed for different combinations of RF and laser fields. The results provide insight into unlocking new opportunities to achieve direct density modulation during electron current emission by optical means.
REFERENCES
1.
K. L.
Jensen
, Introduction to the Physics of Electron Emission
, 1st ed.
(Wiley
, Hoboken
, NJ
, 2017
).2.
A. V.
Burdakov
, A. V.
Arzhannikov
, V. S.
Burmasov
, I. A.
Ivanov
, M. V.
Ivantsivsky
, I. V.
Kandaurov
, S. A.
Kuznetsov
, V. V.
Kurkuchekov
, K. I.
Mekler
, S. V.
Polosatkin
, S. S.
Popov
, V. V.
Postupaev
, A. F.
Rovenskikh
, V. F.
Sklyarov
, M. K. A.
Thumm
, Y. A.
Trunev
, and L. N.
Vyacheslavov
, “Microwave generation during 100
keV electron beam relaxation in GOL-3
,” Fusion Sci. Technol.
63
(1T
), 286
–288
(2013
). 3.
R. J.
England
, R. J.
Noble
, K.
Bane
, D. H.
Dowell
, C.-K.
Ng
, J. E.
Spencer
, S.
Tantawi
, Z.
Wu
, R. L.
Byer
, E.
Peralta
, K.
Soong
, C.-M.
Chang
, B.
Montazeri
, S. J.
Wolf
, B.
Cowan
, J.
Dawson
, W.
Gai
, P.
Hommelhoff
, Y.-C.
Huang
, C.
Jing
, C.
McGuinness
, R. B.
Palmer
, B.
Naranjo
, J.
Rosenzweig
, G.
Travish
, A.
Mizrahi
, L.
Schachter
, C.
Sears
, G. R.
Werner
, and R. B.
Yoder
, “Dielectric laser accelerators
,” Rev. Mod. Phys.
86
(4
), 1337
–1389
(2014
). 4.
T.
Popmintchev
, M.-C.
Chen
, D.
Popmintchev
, P.
Arpin
, S.
Brown
, S.
Ališauskas
, G.
Andriukaitis
, T.
Balčiunas
, O. D.
Mücke
, A.
Pugzlys
, A.
Baltuška
, B.
Shim
, S. E.
Schrauth
, A.
Gaeta
, C.
Hernández-García
, L.
Plaja
, A.
Becker
, A.
Jaron-Becker
, M. M.
Murnane
, and H. C.
Kapteyn
, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers
,” Science
336
(6086
), 1287
–1291
(2012
). 5.
M.
Tu
, B.
Xia
, D. E.
Kravchenko
, M. L.
Tietze
, A. J.
Cruz
, I.
Stassen
, T.
Hauffman
, J.
Teyssandier
, S.
De Feyter
, Z.
Wang
, R. A.
Fischer
, B.
Marmiroli
, H.
Amenitsch
, A.
Torvisco
, M. J.
Velásquez-Hernández
, P.
Falcaro
, and R.
Ameloot
, “Direct x-ray and electron-beam lithography of halogenated zeolitic imidazolate frameworks
,” Nat. Mater.
20
(1
), 93
–99
(2021
). 6.
G. N.
Fursey
, “Field emission in vacuum micro-electronics
,” Appl. Surf. Sci.
215
(1–4
), 113
–134
(2003
). 7.
C. M.
Armstrong
, E. C.
Snively
, M.
Shumail
, C.
Nantista
, Z.
Li
, S.
Tantawi
, B. W.
Loo
, R. J.
Temkin
, R. G.
Griffin
, J.
Feng
, R.
Dionisio
, F.
Mentgen
, N.
Ayllon
, M. A.
Henderson
, and T. P.
Goodman
, “Frontiers in the application of RF vacuum electronics
,” IEEE Trans. Electron Devices
70
, 2643
–2655
(2023
). 8.
P.
Wong
, P.
Zhang
, and J.
Luginsland
, “Recent theory of traveling-wave tubes: A tutorial-review
,” Plasma Res. Express
2
(2
), 023001
(2020
). 9.
D.
Shiffler
, T. K.
Statum
, T. W.
Hussey
, O.
Zhou
, and P.
Mardahl
, Wave Power Electron
(IEEE
, Piscataway
, NJ
, 2005
), p. 691
.10.
Y.
Zhu
and H.
Dürr
, “The future of electron microscopy
,” Phys. Today
68
(4
), 32
–38
(2015
). 11.
A.
Grillo
, J.
Barrat
, Z.
Galazka
, M.
Passacantando
, F.
Giubileo
, L.
Iemmo
, G.
Luongo
, F.
Urban
, C.
Dubourdieu
, and A.
Di Bartolomeo
, “High field-emission current density from β-Ga2O3 nanopillars
,” Appl. Phys. Lett.
114
(19
), 193101
(2019
). 12.
S.
Sun
, X.
Sun
, D.
Bartles
, E.
Wozniak
, J.
Williams
, P.
Zhang
, and C.-Y.
Ruan
, “Direct imaging of plasma waves using ultrafast electron microscopy
,” Struct. Dyn.
7
(6
), 064301
(2020
). 13.
S.
Banerjee
and P.
Zhang
, “Scaling of time-dependent tunneling current in terahertz scanning tunneling microscopes
,” Phys. Rev. Appl.
18
(2
), 024011
(2022
). 14.
H. R.
Kaufman
, The Neutralization of Ion-Rocket Beams
(National Aeronautics and Space Administration
, 1961
).15.
P.
Zhang
and Y. Y.
Lau
, “Ultrafast and nanoscale diodes
,” J. Plasma Phys.
82
(5
), 595820505
(2016
). 16.
J.
Lin
, P. Y.
Wong
, P.
Yang
, Y. Y.
Lau
, W.
Tang
, and P.
Zhang
, “Electric field distribution and current emission in a miniaturized geometrical diode
,” J. Appl. Phys.
121
(24
), 244301
(2017
). 17.
P.
Zhang
, Y. S.
Ang
, A. L.
Garner
, Á.
Valfells
, J. W.
Luginsland
, and L. K.
Ang
, “Space–charge limited current in nanodiodes: Ballistic, collisional, and dynamical effects
,” J. Appl. Phys.
129
(10
), 100902
(2021
). 18.
S.
Banerjee
and P.
Zhang
, “Review of recent studies on nanoscale electrical junctions and contacts: Quantum tunneling, current crowding, and interface engineering
,” J. Vac. Sci. Technol. A
40
(3
), 030802
(2022
). 19.
J.
Benford
, J. A.
Swegle
, and E.
Schamiloglu
, High Power Microwaves
, 3rd ed.
(CRC Press
, 2015
).20.
J. H.
Booske
, “Plasma physics and related challenges of millimeter-wave-to-terahertz and high power microwave generation
,” Phys. Plasmas
15
(5
), 055502
(2008
). 21.
A. S.
Gilmour
, Jr., Principles of Traveling Wave Tubes
(Artech Print on Demand
, Boston
, 1994
).22.
P.
Zhang
, L. K.
Ang
, and A.
Gover
, “Enhancement of coherent Smith–Purcell radiation at terahertz frequency by optimized grating, prebunched beams, and open cavity
,” Phys. Rev. Spec. Top. Accel. Beams
18
(2
), 020702
(2015
). 23.
M. A.
Faisal
and P.
Zhang
, “Grating optimization for Smith–Purcell radiation: Direct correlation between spatial growth rate and starting current
,” IEEE Trans. Electron Devices
70
, 2860
–2863
(2023
). 24.
D. H.
Simon
, B. W.
Hoff
, J. A.
Schrock
, S.
Beeson
, W.
Tang
, P. D.
Lepell
, T.
Montoya
, D. M.
French
, and S. L.
Heidger
, “Experiments on a disk-on-rod traveling wave tube amplifier driven by a nonlinear transmission line modulated electron beam
,” IEEE Trans. Plasma Sci.
50
(2
), 236
–240
(2022
). 25.
V. L.
Granatstein
, R. K.
Parker
, and C. M.
Armstrong
, “Vacuum electronics at the dawn of the twenty-first century
,” Proc. IEEE
87
(5
), 702
–716
(1999
). 26.
M. A.
Kodis
, K. L.
Jensen
, E. G.
Zaidman
, B.
Goplen
, and D. N.
Smithe
, “Operation and optimization of gated field emission arrays in inductive output amplifiers
,” IEEE Trans. Plasma Sci.
24
(3
), 970
–981
(1996
). 27.
G. A.
Espersen
, “Principles of electron tubes including grid-controlled tubes, microwave tubes and gas tubes
,” Proc. IEEE
53
(8
), 1166
(1965
). 28.
D. H.
Simon
, P.
Wong
, D.
Chernin
, Y. Y.
Lau
, B.
Hoff
, P.
Zhang
, C. F.
Dong
, and R. M.
Gilgenbach
, “On the evaluation of pierce parameters C and Q in a traveling wave tube
,” Phys. Plasmas
24
(3
), 033114
(2017
). 29.
A. V.
Haeff
and L. S.
Nergaard
, “A wide-band inductive-output amplifier
,” Proc. IRE
28
(3
), 126
–130
(1940
). 30.
A. J.
Lichtenberg
, “Prebunched beam traveling-wave tube studies
,” IRE Trans. Electron Devices
9
(4
), 345
–351
(1962
). 31.
D. R.
Whaley
, B. M.
Gannon
, C. R.
Smith
, C. M.
Armstrong
, and C. A.
Spindt
, “Application of field emitter arrays to microwave power amplifiers
,” IEEE Trans. Plasma Sci.
28
(3
), 727
–747
(2000
). 32.
D. R.
Whaley
, B. M.
Gannon
, V. O.
Heinen
, K. E.
Kreischer
, C. E.
Holland
, and C. A.
Spindt
, “Experimental demonstration of an emission-gated traveling-wave tube amplifier
,” IEEE Trans. Plasma Sci.
30
(3
), 998
–1008
(2002
). 33.
K. L.
Jensen
, Y. Y.
Lau
, and D. S.
McGregor
, “Analysis of a photon assisted field emission device
,” Appl. Phys. Lett.
77
(4
), 585
–587
(2000
). 34.
C. M.
Armstrong
, “The quest for the ultimate vacuum tube
,” IEEE Spectr.
52
(12
), 28
–51
(2015
). 35.
K. L.
Jensen
, Y. Y.
Lau
, and D.
McGregor
, “Photon assisted field emission from a silicon emitter
,” Solid-State Electron.
45
(6
), 831
–840
(2001
). 36.
P.
Hommelhoff
, Y.
Sortais
, A.
Aghajani-Talesh
, and M. A.
Kasevich
, “Field emission tip as a nanometer source of free electron femtosecond pulses
,” Phys. Rev. Lett.
96
(7
), 077401
(2006
). 37.
R.
Bormann
, M.
Gulde
, A.
Weismann
, S. V.
Yalunin
, and C.
Ropers
, “Tip-enhanced strong-field photoemission
,” Phys. Rev. Lett.
105
(14
), 147601
(2010
). 38.
P.
Tallerico
, R.
Sheffield
, W.
Cornelius
, E.
Gray
, M.
Wilson
, D.
Nguyen
, K.
Meier
, and R.
Stockley
, “An RF-driven lasertron,” in Proceedings of the 1988 Linear Accelerator Conference, Williamsburg, VA, 3-7 October 1988.
39.
E. L.
Garwin
, W. B.
Herrmannsfeldt
, C.
Sinclair
, J. N.
Weaver
, J. J.
Welch
, and P. B.
Wilson
, “An experimental program to build a multimegawatt lasertron for super linear colliders
,” IEEE Trans. Nucl. Sci.
32
(5
), 2906
–2908
(1985
). 40.
W. W.
Tang
, D. A.
Shiffler
, J. R.
Harris
, K. L.
Jensen
, K.
Golby
, M.
LaCour
, and T.
Knowles
, “Field emission characteristics of a small number of carbon fiber emitters
,” AIP Adv.
6
(9
), 095007
(2016
). 41.
W.
Tang
, D.
Shiffler
, K.
Golby
, M.
LaCour
, and T.
Knowles
, “Experimental study of electric field screening by the proximity of two carbon fiber cathodes
,” J. Vac. Sci. Technol. B
30
(6
), 061803
(2012
). 42.
T. A.
Spencer
, K. J.
Hendricks
, M. D.
Haworth
, M. D.
Mitchell
, M. D.
Sena
, M. J.
LaCour
, and D. A.
Shiffler
, “Comparison of carbon fiber and cesium iodide-coated carbon fiber cathodes
,” IEEE Trans. Plasma Sci.
28
(3
), 517
–522
(2000
). 43.
D.
Shiffler
, S.
Fairchild
, W.
Tang
, B.
Maruyama
, K.
Golby
, M.
LaCour
, M.
Pasquali
, and N.
Lockwood
, “Demonstration of an acid-spun single-walled nanotube fiber cathode
,” IEEE Trans. Plasma Sci.
40
(7
), 1871
–1877
(2012
). 44.
S. B.
Fairchild
, J.
Boeckl
, T. C.
Back
, J. B.
Ferguson
, H.
Koerner
, P. T.
Murray
, B.
Maruyama
, M. A.
Lange
, M. M.
Cahay
, N.
Behabtu
, C. C.
Young
, M.
Pasquali
, N. P.
Lockwood
, K. L.
Averett
, G.
Gruen
, and D. E.
Tsentalovich
, “Morphology dependent field emission of acid-spun carbon nanotube fibers
,” Nanotechnology
26
(10
), 105706
(2015
). 45.
P.
Zhang
, S. B.
Fairchild
, T. C.
Back
, and Y.
Luo
, “Field emission from carbon nanotube fibers in varying anode-cathode gap with the consideration of contact resistance
,” AIP Adv.
7
(12
), 125203
(2017
). 46.
P.
Zhang
, J.
Park
, S.
Fairchild
, N.
Lockwood
, Y.
Lau
, J.
Ferguson
, and T.
Back
, “Temperature comparison of looped and vertical carbon nanotube fibers during field emission
,” Appl. Sci.
8
(7
), 1175
(2018
). 47.
S. B.
Fairchild
, P.
Zhang
, J.
Park
, T. C.
Back
, D.
Marincel
, Z.
Huang
, and M.
Pasquali
, “Carbon nanotube fiber field emission array cathodes
,” IEEE Trans. Plasma Sci.
47
(5
), 2032
–2038
(2019
). 48.
S. B.
Fairchild
, C. E.
Amanatides
, T. A.
De Assis
, P. T.
Murray
, D.
Tsentalovich
, J. L.
Ellis
, S.
Portillo
, S. R.
Kanel
, J. S.
Bulmer
, J.
Park
, G.
Dion
, and J. J.
Boeckl
, “Field emission cathodes made from knitted carbon nanotube fiber fabrics
,” J. Appl. Phys.
133
(9
), 094302
(2023
). 49.
S.
Ji
, L.
Piazza
, G.
Cao
, S. T.
Park
, B. W.
Reed
, D. J.
Masiel
, and J.
Weissenrieder
, “Influence of cathode geometry on electron dynamics in an ultrafast electron microscope
,” Struct. Dyn.
4
(5
), 054303
(2017
). 50.
P.
Zhang
and Y. Y.
Lau
, “Ultrafast strong-field photoelectron emission from biased metal surfaces: Exact solution to time-dependent Schrödinger equation
,” Sci. Rep.
6
(1
), 19894
(2016
). 51.
Y.
Luo
and P.
Zhang
, “Analysis of two-color laser-induced electron emission from a biased metal surface using an exact quantum mechanical solution
,” Phys. Rev. Appl.
12
(4
), 044056
(2019
). 52.
Y.
Luo
, Y.
Zhou
, and P.
Zhang
, “Few-cycle optical-field-induced photoemission from biased surfaces: An exact quantum theory
,” Phys. Rev. B
103
(8
), 085410
(2021
). 53.
Y.
Zhou
and P.
Zhang
, “Unraveling quantum pathways interference in two-color coherent control of photoemission with bias voltages
,” Phys. Rev. B
106
(8
), 085402
(2022
). 54.
J. W.
Lewellen
and J.
Noonan
, “Field-emission cathode gating for rf electron guns
,” Phys. Rev. Spec. Top. Accel. Beams
8
(3
), 033502
(2005
). 55.
G. A.
Mesyats
, “Ecton mechanism of the cathode spot phenomena in a vacuum arc
,” IEEE Trans. Plasma Sci.
41
(4
), 676
–694
(2013
). 56.
Y.
Zhou
and P.
Zhang
, “A quantum model for photoemission from metal surfaces and its comparison with the three-step model and Fowler–DuBridge model
,” J. Appl. Phys.
127
(16
), 164903
(2020
). 57.
Y.
Zhou
and P.
Zhang
, “Quantum efficiency of photoemission from biased metal surfaces with laser wavelengths from UV to NIR
,” J. Appl. Phys.
130
(6
), 064902
(2021
). 58.
Y.
Zhou
and P.
Zhang
, “Theory of laser-induced photoemission from a metal surface with nanoscale dielectric coating
,” J. Appl. Phys.
131
(6
), 064903
(2022
). 59.
X.
Xiong
, Y.
Zhou
, Y.
Luo
, X.
Li
, M.
Bosman
, L. K.
Ang
, P.
Zhang
, and L.
Wu
, “Plasmon-enhanced resonant photoemission using atomically thick dielectric coatings
,” ACS Nano
14
(7
), 8806
–8815
(2020
). 60.
Y.
Luo
, J.
Luginsland
, and P.
Zhang
, “Interference modulation of photoemission from biased metal cathodes driven by two lasers of the same frequency
,” AIP Adv.
10
(7
), 075301
(2020
). 61.
Y.
Luo
and P.
Zhang
, “Ultrafast strong-field photoelectron emission due to two-color laser fields
,” Phys. Rev. B
98
(16
), 165442
(2018
). 62.
Y.
Zhou
and P.
Zhang
, “Theory of field emission from dielectric coated surfaces
,” Phys. Rev. Res.
2
(4
), 043439
(2020
). 63.
Y.
Luo
and P.
Zhang
, “Ultrafast optical-field-induced photoelectron emission in a vacuum nanoscale gap: An exact analytical formulation
,” Appl. Phys. Lett.
119
(19
), 194101
(2021
). 64.
Y.
Luo
and P.
Zhang
, “Optical-field-induced electron emission in a dc-biased nanogap
,” Phys. Rev. Appl.
17
(4
), 044008
(2022
). 65.
R. G.
Forbes
, “Physics of generalized Fowler–Nordheim-type equations
,” J. Vac. Sci. Technol. B
26
(2
), 788
(2008
). 66.
S.
Keramati
, A.
Passian
, V.
Khullar
, J.
Beck
, C.
Uiterwaal
, and H.
Batelaan
, “Surface plasmon enhanced fast electron emission from metallised fibre optic nanotips
,” New J. Phys.
22
(8
), 083069
(2020
). 67.
Y.
Zhou
, R.
Ahsan
, H. U.
Chae
, R.
Kapadia
, and P.
Zhang
, “Theoretical analysis of resonant tunneling enhanced field emission
,” Phys. Rev. Appl.
20
(1
), 014043
(2023
). 68.
J. H.
Bechtel
, “Heating of solid targets with laser pulses
,” J. Appl. Phys.
46
(4
), 1585
–1593
(1975
). 69.
R. H.
Fowler
and L.
Nordheim
, “Electron emission in intense electric fields
,” Proc. R. Soc. Lond. Ser. Contain. Pap. Math. Phys. Character
119
(781
), 173
–181
(1928
). 70.
P.
Zhang
, Á.
Valfells
, L. K.
Ang
, J. W.
Luginsland
, and Y. Y.
Lau
, “100 years of the physics of diodes
,” Appl. Phys. Rev.
4
(1
), 011304
(2017
). 71.
P.
Zhang
, “Scaling for quantum tunneling current in nano- and subnano-scale plasmonic junctions
,” Sci. Rep.
5
(1
), 9826
(2015
). 72.
S.
Banerjee
and P.
Zhang
, “A generalized self-consistent model for quantum tunneling current in dissimilar metal-insulator-metal junction
,” AIP Adv.
9
(8
), 085302
(2019
). 73.
Y. L.
Liu
, P.
Zhang
, S. H.
Chen
, and L. K.
Ang
, “Maximal charge injection of consecutive electron pulses with uniform temporal pulse separation
,” Phys. Plasmas
22
(8
), 084504
(2015
). 74.
Y. L.
Liu
, P.
Zhang
, S. H.
Chen
, and L. K.
Ang
, “Maximal charge injection of a uniform separated electron pulse train in a drift space
,” Phys. Rev. Spec. Top. Accel. Beams
18
(12
), 123402
(2015
). 75.
C.
Kaur
, K.
Rambabu
, and R.
Fedosejevs
, “High-current space-charge-limited pulses using ultrashort laser pulses
,” Phys. Rev. E
106
(5
), 055203
(2022
). 76.
M. A.
McEver
, “Adaptive feedback control of optical jitter using Q-parameterization
,” Opt. Eng.
43
(4
), 904
(2004
). 77.
D.
Kim
, J. J.
Kim
, D.
Frist
, M.
Nagashima
, and B.
Agrawal
, “High energy laser testbed for accurate beam pointing control
,” Proc. SPIE
7587
, 75870G
(2010
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.
