Shocks in supersonic flows offer both high density and sharp density gradients that are used, for instance, for gradient injection in laser-plasma accelerators. We report on a parametric study of oblique shocks created by inserting a straight axisymmetric section at the end of a supersonic “de Laval” nozzle. The effect of different parameters, such as the throat diameter and straight section length on the shock position and density, is studied through computational fluid dynamics (CFD) simulations. Experimental characterizations of a shocked nozzle are compared to CFD simulations and found to be in good agreement. We then introduce a newly designed asymmetric shocked gas jet, where the straight section is only present on one lateral side of the nozzle, thus providing a gas profile well adapted for density transition injection. In this case, full-3D fluid simulations and experimental measurements are compared and show excellent agreement.

1.
T.
Tajima
and
J. M.
Dawson
, “
Laser electron accelerator
,”
Phys. Rev. Lett.
43
,
267
270
(
1979
).
2.
E.
Esarey
,
C. B.
Schroeder
, and
W. P.
Leemans
, “
Physics of laser-driven plasma-based electron accelerators
,”
Rev. Mod. Phys.
81
,
1229
1285
(
2009
).
3.
A.
Rousse
,
K. T.
Phuoc
,
R.
Shah
,
A.
Pukhov
,
E.
Lefebvre
,
V.
Malka
,
S.
Kiselev
,
F.
Burgy
,
J.-P.
Rousseau
,
D.
Umstadter
, and
D.
Hulin
, “
Production of a keV x-ray beam from synchrotron radiation in relativistic laser-plasma interaction
,”
Phys. Rev. Lett.
93
,
135005
(
2004
).
4.
S.
Kneip
,
C.
McGuffey
,
J. L.
Martins
,
S. F.
Martins
,
C.
Bellei
,
V.
Chvykov
,
F.
Dollar
,
R.
Fonseca
,
C.
Huntington
,
G.
Kalintchenko
,
A.
Maksimchuk
,
S. P. D.
Mangles
,
T.
Matsuoka
,
S. R.
Nagel
,
C. A. J.
Palmer
,
J.
Schreiber
,
K.
Ta Phuoc
,
A. G. R.
Thomas
,
V.
Yanovsky
,
L. O.
Silva
,
K.
Krushelnick
, and
Z.
Najmudin
,
Nat. Phys.
6
,
980
983
(
2010
).
5.
K.
Ta Phuoc
,
S.
Corde
,
C.
Thaury
,
V.
Malka
,
A.
Tafzi
,
J.-P.
Goddet
,
R. C.
Shah
,
S.
Sebban
, and
A.
Rousse
, “
All-optical Compton gamma-ray source
,”
Nat. Photonics
6
,
308
311
(
2012
).
6.
C. B.
Schroeder
,
E.
Esarey
,
C. G. R.
Geddes
,
C.
Benedetti
, and
W. P.
Leemans
, “
Physics considerations for laser-plasma linear colliders
,”
Phys. Rev. Spec. Top.-Accel. Beams
13
,
101301
(
2010
).
7.
Z.-H.
He
,
B.
Beaurepaire
,
J. A.
Nees
,
G.
Gallé
,
S. A.
Scott
,
J. R. S.
Pérez
,
M. G.
Lagally
,
K.
Krushelnick
,
A. G. R.
Thomas
, and
J.
Faure
, “
Capturing structural dynamics in crystalline silicon using chirped electrons from a laser wakefield accelerator
,”
Sci. Rep.
6
,
36224
(
2016
).
8.
J.
Faure
,
B.
van der Geer
,
B.
Beaurepaire
,
G.
Gallé
,
A.
Vernier
, and
A.
Lifschitz
, “
Concept of a laser-plasma-based electron source for sub-10-fs electron diffraction
,”
Phys. Rev. Accel. Beams
19
,
021302
(
2016
).
9.
O.
Rigaud
,
N. O.
Fortunel
,
P.
Vaigot
,
E.
Cadio
,
M. T.
Martin
,
O.
Lundh
,
J.
Faure
,
C.
Rechatin
,
V.
Malka
, and
Y. A.
Gauduel
, “
Exploring ultrashort high-energy electron-induced damage in human carcinoma cells
,”
Cell Death Dis.
1
,
e73
(
2010
).
10.
O.
Lundh
,
C.
Rechatin
,
J.
Faure
,
A.
Ben-Ismaïl
,
J.
Lim
,
C.
De Wagter
,
W.
De Neve
, and
V.
Malka
, “
Comparison of measured with calculated dose distribution from a 120-MeV electron beam from a laser-plasma accelerator
,”
Med. Phys.
39
,
3501
3508
(
2012
).
11.
S.
Bulanov
,
N.
Naumova
,
F.
Pegoraro
, and
J.
Sakai
, “
Particle injection into the wave acceleration phase due to nonlinear wake wave breaking
,”
Phys. Rev. E
58
,
R5257
R5260
(
1998
).
12.
P.
Tomassini
,
M.
Galimberti
,
A.
Giulietti
,
D.
Giulietti
,
L. A.
Gizzi
,
L.
Labate
, and
F.
Pegoraro
, “
Production of high-quality electron beams in numerical experiments of laser wakefield acceleration with longitudinal wave breaking
,”
Phys. Rev. Spec. Top.-Accel. Beams
6
,
121301
(
2003
).
13.
H.
Suk
,
N.
Barov
,
J. B.
Rosenzweig
, and
E.
Esarey
, “
Plasma electron trapping and acceleration in a plasma wake field using a density transition
,”
Phys. Rev. Lett.
86
,
1011
1014
(
2001
).
14.
J. U.
Kim
,
N.
Hafz
, and
H.
Suk
, “
Electron trapping and acceleration across a parabolic plasma density profile
,”
Phys. Rev. E
69
,
026409
(
2004
).
15.
T.-Y.
Chien
,
C.-L.
Chang
,
C.-H.
Lee
,
J.-Y.
Lin
,
J.
Wang
, and
S.-Y.
Chen
, “
Spatially localized self-injection of electrons in a self-modulated laser-wakefield accelerator by using a laser-induced transient density ramp
,”
Phys. Rev. Lett.
94
,
115003
(
2005
).
16.
J.
Faure
,
C.
Rechatin
,
O.
Lundh
,
L.
Ammoura
, and
V.
Malka
, “
Injection and acceleration of quasimonoenergetic relativistic electron beams using density gradients at the edges of a plasma channel
,”
Phys. Plasmas
17
,
083107
(
2010
).
17.
K.
Schmid
,
A.
Buck
,
C. M. S.
Sears
,
J. M.
Mikhailova
,
R.
Tautz
,
D.
Herrmann
,
M.
Geissler
,
F.
Krausz
, and
L.
Veisz
, “
Density-transition based electron injector for laser driven wakefield accelerators
,”
Phys. Rev. Spec. Top.-Accel. Beams
13
,
091301
(
2010
).
18.
C.
Thaury
,
E.
Guillaume
,
A.
Lifschitz
,
K.
Ta Phuoc
,
M.
Hansson
,
G.
Grittani
,
J.
Gautier
,
J.-P.
Goddet
,
A.
Tafzi
,
O.
Lundh
, and
V.
Malka
, “
Shock assisted ionization injection in laser-plasma accelerators
,”
Sci. Rep.
5
,
16310
(
2015
).
19.
K. K.
Swanson
,
H.-E.
Tsai
,
S. K.
Barber
,
R.
Lehe
,
H.-S.
Mao
,
S.
Steinke
,
J.
van Tilborg
,
K.
Nakamura
,
C. G. R.
Geddes
,
C. B.
Schroeder
,
E.
Esarey
, and
W. P.
Leemans
, “
Control of tunable, monoenergetic laser-plasma-accelerated electron beams using a shock-induced density downramp injector
,”
Phys. Rev. Accel. Beams
20
,
051301
(
2017
).
20.
D.
Haberberger
,
S.
Tochitsky
,
F.
Fiuza
,
C.
Gong
,
R. A.
Fonseca
,
L. O.
Silva
,
W. B.
Mori
, and
C.
Joshi
, “
Collisionless shocks in laser-produced plasma generate monoenergetic high-energy proton beams
,”
Nat. Phys.
8
,
95
99
(
2012
).
21.
T.
Nakamura
,
S. V.
Bulanov
,
T. Z.
Esirkepov
, and
M.
Kando
, “
High-energy ions from near-critical density plasmas via magnetic vortex acceleration
,”
Phys. Rev. Lett.
105
,
135002
(
2010
).
22.
F.
Sylla
,
A.
Flacco
,
S.
Kahaly
,
M.
Veltcheva
,
A.
Lifschitz
,
V.
Malka
,
E.
d’Humières
,
I.
Andriyash
, and
V.
Tikhonchuk
, “
Short intense laser pulse collapse in near-critical plasma
,”
Phys. Rev. Lett.
110
,
085001
(
2013
).
23.
L.
Fan-Chiang
,
H.-S.
Mao
,
H.-E.
Tsai
,
T.
Ostermayr
,
K. K.
Swanson
,
S. K.
Barber
,
S.
Steinke
,
J.
van Tilborg
,
C. G. R.
Geddes
, and
W. P.
Leemans
, “
Gas density structure of supersonic flows impinged on by thin blades for laser–plasma accelerator targets
,”
Phys. Fluids
32
,
066108
(
2020
).
24.
F.
Mollica
, “
Ultra-intense laser-plasma interaction at near-critical density for ion acceleration
,” Ph.D. thesis,
Université Paris Saclay
,
2016
.
25.
L.
Rovige
,
J.
Huijts
,
I.
Andriyash
,
A.
Vernier
,
V.
Tomkus
,
V.
Girdauskas
,
G.
Raciukaitis
,
J.
Dudutis
,
V.
Stankevic
,
P.
Gecys
,
M.
Ouille
,
Z.
Cheng
,
R.
Lopez-Martens
, and
J.
Faure
, “
Demonstration of stable long-term operation of a kilohertz laser-plasma accelerator
,”
Phys. Rev. Accel. Beams
23
,
093401
(
2020
).
26.
R. D.
Zucker
and
O.
Biblarz
,
Fundamentals of Gas Dynamics
(
John Wiley & Sons
,
2002
).
27.
S.
Semushin
and
V.
Malka
, “
High density gas jet nozzle design for laser target production
,”
Rev. Sci. Instrum.
72
,
2961
2965
(
2001
).
28.
K.
Schmid
and
L.
Veisz
, “
Supersonic gas jets for laser-plasma experiments
,”
Rev. Sci. Instrum.
83
,
053304
(
2012
).
29.
H.
Liepmann
and
A.
Roshko
,
Elements of Gas Dynamics
, Dover Books on Aeronautical Engineering (
Dover Publications
,
2013
).
30.
R.
Courant
and
K. O.
Friedrichs
,
Supersonic Flow and Shock Waves
(
Interscience Publishers
,
1948
).
31.
D. C.
Wilcox
 et al,
Turbulence Modeling for CFD
(
DCW Industries
,
La Canada, CA
,
1998
), Vol. 2.
32.
F. R.
Menter
, “
Two-equation eddy-viscosity turbulence models for engineering applications
,”
AIAA J.
32
,
1598
1605
(
1994
).
33.
J.
Primot
and
L.
Sogno
, “
Achromatic three-wave (or more) lateral shearing interferometer
,”
J. Opt. Soc. Am. A
12
,
2679
2685
(
1995
).
34.
F.
Böhle
,
M.
Kretschmar
,
A.
Jullien
,
M.
Kovacs
,
M.
Miranda
,
R.
Romero
,
H.
Crespo
,
U.
Morgner
,
P.
Simon
,
R.
Lopez-Martens
, and
T.
Nagy
, “
Compression of CEP-stable multi-mJ laser pulses down to 4 fs in long hollow fibers
,”
Laser Phys. Lett.
11
,
095401
(
2014
).
35.
A.
Marcinkevičius
,
S.
Juodkazis
,
M.
Watanabe
,
M.
Miwa
,
S.
Matsuo
,
H.
Misawa
, and
J.
Nishii
, “
Femtosecond laser-assisted three-dimensional microfabrication in silica
,”
Opt. Lett.
26
,
277
279
(
2001
).
36.
V.
Tomkus
,
V.
Girdauskas
,
J.
Dudutis
,
P.
Gečys
,
V.
Stankevič
, and
G.
Račiukaitis
, “
High-density gas capillary nozzles manufactured by hybrid 3D laser machining technique from fused silica
,”
Opt. Express
26
,
27965
27977
(
2018
).
37.
T.
Katsouleas
, “
Physical mechanisms in the plasma wake-field accelerator
,”
Phys. Rev. A
33
,
2056
2064
(
1986
).
38.
P.
Sprangle
,
B.
Hafizi
,
J. R.
Peñano
,
R. F.
Hubbard
,
A.
Ting
,
C. I.
Moore
,
D. F.
Gordon
,
A.
Zigler
,
D.
Kaganovich
, and
T. M.
Antonsen
, “
Wakefield generation and GeV acceleration in tapered plasma channels
,”
Phys. Rev. E
63
,
056405
(
2001
).
39.
E.
Guillaume
,
A.
Döpp
,
C.
Thaury
,
K.
Ta Phuoc
,
A.
Lifschitz
,
G.
Grittani
,
J.-P.
Goddet
,
A.
Tafzi
,
S. W.
Chou
,
L.
Veisz
, and
V.
Malka
, “
Electron rephasing in a laser-wakefield accelerator
,”
Phys. Rev. Lett.
115
,
155002
(
2015
).
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