U.S. patent application number 15/152627 was filed with the patent office on 2016-11-24 for colliding jets laser guiding structure.
This patent application is currently assigned to The Government of the United States of America, as represented by the Secretary of the Navy. The applicant listed for this patent is The Government of the United States of America, as represented by the Secretary of the Navy, The Government of the United States of America, as represented by the Secretary of the Navy. Invention is credited to Yu-hsin Chen, Daniel F. Gordon, Michael H. Helle, Dmitri Kaganovich, John Palastro, Antonio C. Ting.
Application Number | 20160345420 15/152627 |
Document ID | / |
Family ID | 57234912 |
Filed Date | 2016-11-24 |
United States Patent
Application |
20160345420 |
Kind Code |
A1 |
Kaganovich; Dmitri ; et
al. |
November 24, 2016 |
Colliding Jets Laser Guiding Structure
Abstract
A plurality of gas jet nozzles having equal angular separation
around a central axis eject gas flows towards the central axis. The
gas flows collide and form a gas channel from the neutral gas, the
gas channel having a gas density depression at the center of the
intersecting gas flow, where the gas density depression is
surrounded by a higher density gaseous wall along the central axis.
Ionization of the gas in the center produces a plasma channel that
can guide a laser pulse fired into the gas along the central axis.
The geometric arrangement of the gas jets and/or the backing
pressure of the gas flows are configured to produce a gas channel
having a predetermined density profile such that the ionized gas
forms a plasma channel laser guiding structure configured to guide
a laser pulse having predetermined spatial parameters.
Inventors: |
Kaganovich; Dmitri;
(Potomac, MD) ; Helle; Michael H.; (Arlington,
VA) ; Palastro; John; (College Park, MD) ;
Ting; Antonio C.; (Silver Spring, MD) ; Gordon;
Daniel F.; (Alexandria, VA) ; Chen; Yu-hsin;
(Fairfax, VA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
The Government of the United States of America, as represented by
the Secretary of the Navy |
Arlington |
VA |
US |
|
|
Assignee: |
The Government of the United States
of America, as represented by the Secretary of the Navy
Arlington
VA
|
Family ID: |
57234912 |
Appl. No.: |
15/152627 |
Filed: |
May 12, 2016 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62166197 |
May 26, 2015 |
|
|
|
62164627 |
May 21, 2015 |
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H05H 1/00 20130101; Y02E
30/10 20130101; H05H 1/54 20130101; H05H 15/00 20130101; H05H 1/48
20130101; H05H 1/24 20130101; G21B 3/008 20130101 |
International
Class: |
H05H 1/48 20060101
H05H001/48 |
Claims
1. A method for forming a laser guiding structure, comprising:
activating a plurality of gas flows from a corresponding plurality
of gas nozzles arranged at equal angular intervals around a central
axis, the gas nozzles being configured to produce a plurality of
gas flows that intersect with one another along the central axis to
controllably form a gas channel from the neutral gas, the gas
channel having gas density depression at a center of the gas
channel; and at time t1, firing an ionizing pulse through the gas
channel at the gas density depression to ionize the gas channel;
wherein at least one of a geometric configuration of the gas
nozzles and a backing pressure of the gas flows is configured to
cause the gas channel to have a predetermined gas density profile
such that the ionized gas channel forms a plasma channel having a
predetermined spatial profile, the plasma channel forming a laser
guiding structure configured to guide a laser pulse having
predetermined spatial parameters fired into the gas along the
central axis at time t2.
2. The method according to claim 1, wherein the ionizing pulse is a
laser pulse fired through the gas density depression at time
t1.
3. The method according to claim 1, wherein the ionizing pulse is
an electrical discharge fired through the gas density depression at
time t1.
4. The method according to claim 1, wherein the gas flows from all
of the gas nozzles are at the same pressure.
5. The method according to claim 1, wherein a gas flow from a first
one of the gas nozzles is at a first pressure and a gas flow from a
second one of the gas nozzles is at a second pressure, the first
pressure being different from the second pressure.
6. The method according to claim 1, wherein the gas flows from all
of the gas nozzles are activated simultaneously.
7. The method according to claim 1, wherein a gas flow from a first
one of the gas nozzles is activated at a first time and a gas flow
from a second one of the gas nozzles is activated at a second time,
the first time being different from the second time, the method
further comprising creating a longitudinal gas flow through the gas
channel to cause the gas to experience a spiraling motion and
create a horizontally and vertically stable gas density depression
in the gas channel.
8. The method according to claim 7, wherein the longitudinal gas
flow is created by pumping the intersecting gases through the gas
channel.
9. The method according to claim 7, wherein the longitudinal gas
flow is created by aiming the gas jets towards a direction of the
longitudinal gas flow.
10. The method according to claim 1, wherein the gas nozzles are
arranged so that the gas flows intersect head-on to produce a gas
channel having a predetermined flat-top gas density profile.
11. The method according to claim 1, wherein the gas nozzles are
arranged so that the intersecting gas flows do not intersect
directly head-on but are offset from one another to produce a gas
channel having a predetermined parabolic gas density profile.
12. The method according to claim 11, the method further comprising
creating a longitudinal gas flow through the gas channel.
13. The method according to claim 11, wherein the longitudinal gas
flow is created by pumping the intersecting gases through the gas
channel.
14. The method according to claim 11, wherein the longitudinal gas
flow is created by aiming the gas jets towards a direction of the
longitudinal gas flow.
15. The method according to claim 1, wherein a spatial profile of
the plasma channel laser guiding structure is further tuned by
tuning at least one parameter of the ionizing pulse fired through
the gas channel.
16. The method according to claim 15, wherein the spatial profile
of the plasma channel laser guiding structure is tuned by tuning a
timing of the ionizing pulse fired through the gas channel.
Description
CROSS-REFERENCE
[0001] This Application is a Non-Provisional of and claims the
benefit of priority under 35 U.S.C. .sctn.119 based on Provisional
Application No. 62/164,627 filed on May 21, 2015 and Provisional
Application 62/166,197 filed on May 26, 2016. The Provisional
Applications and all references cited herein are hereby
incorporated by reference into the present disclosure in their
entirety.
TECHNICAL FIELD
[0002] The present invention relates to plasma waveguides and their
formation.
BACKGROUND
[0003] In applications requiring high intensity laser-plasma
interactions, it is often desirable to maintain high optical
intensity over long interaction distances. Conventional optical
components such as mirrors and lenses cannot operate at laser
intensities above the damage threshold for the materials forming
these components. As a result, such optical elements must be placed
far from the laser focus, limiting the interaction distance of the
focused pulse to the Rayleigh range.
[0004] This limitation can be overcome by focusing the laser beam
into a plasma channel consisting of a preformed plasma having a
minimum density in the center, for example, a plasma having a
parabolic radial density profile. The plasma channel acts as a
waveguide for the laser pulse combating diffraction and maintaining
the pulse intensity over an extended distance. See C. G. Durfee and
H. M. Milchberg, "Light Pipe for High Intensity Laser Pulses,"
Phys. Rev. Lett. 71, 2409 (1993) and D. Kaganovich et al., "High
efficiency guiding of terawatt subpicosecond laser pulses in a
capillary discharge plasma channel", Phys. Rev. E, 59, R4769,
(1999) ("Kaganovich 1999"); see also T. R. Clark and H. M.
Milchberg, "Time- and Space-Resolved Density Evolution of the
Plasma Waveguide," Phys. Rev. Lett. 78, 2373 (1997); and A. Butler,
D. J. Spence, and S. M. Hooker, Guiding of High-Intensity Laser
Pulses with a Hydrogen-Filled Capillary Discharge Waveguide," Phys.
Rev. Lett. 89, 185003 (2002).
[0005] Plasma-channel guiding of ultrashort laser pulses is a key
component for laser-based particle acceleration techniques such as
laser wakefield acceleration (LWFA). See G. M. Mourou, T. Tajima,
and S. Bulanov, "Optics in the relativistic regime," Rev. Mod.
Phys. 78, 309 (2006). LWFA can produce high-quality, low-emittance,
ultrashort bunches of mono-energetic electrons. See V. Malka,
"Laser plasma accelerators," Phys. Plasmas 19, 055501 (2012).
However, several significant technical challenges still separate
LWFA from conventional radio-frequency (RF) accelerators in
particular, maintaining the driving laser pulse intensity over a
long (>10 cm) distance in a low (.ltoreq.1019 cm.sup.-3) plasma
density.
[0006] Plasma channel guiding of laser pulses has been demonstrated
experimentally using channels created by one of two techniques. The
such technique uses solid wall structures based on capillary
discharges. See A. Butler, D. J. Spence, and S. M. Hooker, "Guiding
of High-Intensity Laser Pulses with a Hydrogen-Filled Capillary
Discharge Waveguide," Phys. Rev. Lett. 89, 185003 (2002); see also
Kaganovich 1999, supra. The second technique uses wall-free
channels based on axicon-focused lasers. See Durfee, supra, and
Clark, supra. In both cases, the waveguide is initiated by the
on-axis heating of a uniform cold plasma column or neutral gas. Hot
gas near the axis expands radially, forming a hollow density
channel suitable for guiding.
[0007] The capillary discharge technique for creation of a plasma
guiding channel uses a dielectric tube several hundred microns in
diameter. See Y. Ehrlich, A. Zigler, C. Cohen, J. Krall, and P.
Sprangle, "Guiding of High Intensity Laser Pulses in Straight and
Curved Plasma Channel Experiments," Phys. Rev. Lett. 77, 4186
(1996). The capillary can be back-filled with gas (see Butler,
supra) or filled with wall material ablated when a high voltage
breakdown launches from a pair of electrodes located at each end.
See D. Kaganovich, P. Sasorov, Y. Ehrlich, C. Cohen, and A. Zigler,
"Investigations of double capillary discharge scheme for production
of wave guide in plasma," Appl. Phys. Lett. 71, 2925 (1997)
("Kaganovich 1997"). This produces collisional heating near the
axis while the region near the wall stays relatively cold, setting
up conditions for hollow plasma channel formation.
[0008] The wall-free techniques employ a high energy, long laser
pulse to ionize and heat a plasma column produced from either
clustered (see A. J. Goers, S. J. Yoon, J. A. Elle, G. A. Hine, and
H. M. Milchberg, "Laser wakefield acceleration of electrons with
ionization injection in a pure N5+ plasma waveguide," Applied
Physics Letters 104, 214105 (2014)), or un-clustered (see Geddes,
supra) gas jets. In order to produce an axially extended channel,
the hydrodynamic heater pulse must be line-focused into the gas
column by either an axicon (conical lens), see Durfee, supra, or a
cylindrical focusing optic, see Geddes, supra.
[0009] Creation of long channels requires high laser energy and
precise co-linear alignment, making this scheme more difficult to
implement than capillary channels. For shorter distances (one
centimeter or less), a self-guided laser in clustered gas can be
used to initiate a shock wave-based guiding channel. See V.
Kumarappan, K. Y. Kim, and H. M. Milchberg, "Guiding of Intense
Laser Pulses in Plasma Waveguides Produced from Efficient,
Femtosecond End-Pumped Heating of Clustered Gases, Phys. Rev. Lett.
94, 205004 (2005).
[0010] The current world record for LWFA electron energy, 4.2 GeV,
was demonstrated using a 9-cm long capillary discharged waveguide.
See W. P. Leemans, A. J. Gonsalves, H.-S. Mao, K. Nakamura, C.
Benedetti, C. B. Schroeder, C s. Toth, J. Daniels, D. E.
Mittelberger, S. S. Bulanov, J.-L. Vay, C. G. R. Geddes, and E.
Esarey, "Multi-GeV Electron Beams from Capillary-Discharge-Guided
Subpetawatt Laser Pulses in the Self-Trapping Regime," Phys. Rev.
Lett. 113, 245002 (2014). While in principle, a discharge capillary
could be extended beyond 10 cm, neither effective guiding nor
acceleration has been demonstrated at such lengths. It appears that
the limitation is discharge formation, but this remains poorly
understood due to difficulties in diagnosing the plasma within a
capillary. Standard diagnostic techniques, such as optical
interferometry, cannot be used to transversely probe the plasma
within the capillary. This also makes it difficult to monitor the
performance of the waveguide. Additionally, the dielectric wall is
subject to damage by the laser field, discharge current, and
plasma.
SUMMARY
[0011] This summary is intended to introduce, in simplified form, a
selection of concepts that are further described in the Detailed
Description. This summary is not intended to identify key or
essential features of the claimed subject matter, nor is it
intended to be used as an aid in determining the scope of the
claimed subject matter. Instead, it is merely presented as a brief
overview of the subject matter described and claimed herein.
[0012] The present invention provides a method for creating a
"wall-free" pre-formed gas or plasma waveguide using several
colliding gas jets.
[0013] The present invention provides a guiding channel for
propagation of a laser beam. In accordance with the present
invention, a plurality of gas jet nozzles having equal angular
separation around a central axis eject gas flows towards the
central axis. The gas flows collide and form a gas channel from the
neutral gas, the gas channel having a gas density minimum or
"depression" at the center of the intersecting gas flow, where the
gas density minimum is surrounded by a higher density gaseous wall
along the central axis. Ionization of the gas in the center
produces a plasma channel that can guide a laser pulse fired into
the gas along the central axis. In accordance with the present
invention, the geometric arrangement of the gas jets and/or the
backing pressure of the gas flows are configured to produce a gas
channel having a predetermined density profile such that the
ionized gas forms a plasma channel laser guiding structure
configured to guide a laser pulse having predetermined spatial
parameters.
BRIEF DESCRIPTION OF THE DRAWINGS
[0014] FIG. 1 is a block drawing illustrating aspects of an
exemplary embodiment of a method for forming a wall-free plasma
waveguide using colliding gas jets in accordance with the present
invention.
[0015] FIG. 2 is a block diagram illustrating an exemplary
embodiment of multi-nozzle gas jets that can be used to form a
wall-free plasma waveguide in accordance with the present
invention.
[0016] FIGS. 3A-3C are plots illustrating aspects of a wall-free
plasma waveguide formed by colliding gas jets in accordance with
the present invention.
[0017] FIGS. 4A and 4B are plots illustrating the effects of
differences in gas jet pressure in the formation of a wall-free
plasma waveguide by colliding gas jets in accordance with the
present invention.
[0018] FIGS. 5A and 5B are plots illustrating aspects of gas jet
time differentials in the formation of a wall-free plasma waveguide
by colliding gas jets in accordance with the present invention.
[0019] FIGS. 6A and 6B are plots illustrating aspects of a
wall-free plasma waveguide formed by offset colliding gas jets in
accordance with the present invention.
[0020] FIGS. 7A and 7B are plots illustrating the manner in which
the gas density profile scales with the gas pressure in a method
for forming a wall-free plasma waveguide by means of colliding gas
jets in accordance with the present invention.
DETAILED DESCRIPTION
[0021] The aspects and features of the present invention summarized
above can be embodied in various forms. The following description
shows, by way of illustration, combinations and configurations in
which the aspects and features can be put into practice. It is
understood that the described aspects, features, and/or embodiments
are merely examples, and that one skilled in the art may utilize
other aspects, features, and/or embodiments or make structural and
functional modifications without departing from the scope of the
present disclosure.
[0022] The present invention provides a new method for producing a
wall-less preformed plasma waveguide. In the method for producing a
plasma waveguide in accordance with the present invention,
colliding gas streams are used to create a hollow gas channel that
is then ionized by an ionizing laser pulse or by any other suitable
ionization mechanism to form a plasma guiding channel within the
gas that can guide a subsequent main propagating laser pulse. In
some cases the same pulse can serve as both the ionizing pulse and
the main propagating pulse.
[0023] Aspects of the method for forming a plasma waveguide in
accordance with the present invention are illustrated in FIG. 1. In
accordance with the present invention, three or more gas jet
nozzles having equal angular separation around a central axis,
e.g., gas jet nozzles 101a-101d having a 90.degree. separation from
one another, eject gas flows, often referred to herein as "gas
jets," towards the central axis. The gas jets are configured to
collide with one another so that the colliding jets form
symmetrical gas channel 102 from the neutral, i.e., unionized, gas
around the central axis. The geometric arrangement of the gas jet
nozzles can be configured so that the gas channel will have a
predetermined gas density profile that can form a plasma channel
suitable for guiding a laser beam having predetermined geometric
parameters. Thus, as described below, in some cases the nozzles can
be configured to produce a gas channel 102 having a cylindrically
symmetric density profile which can enable the formation of a laser
guiding channel suitable for the propagation of a laser beam having
a Bessel profile, while in other cases the nozzles can be
configured to produce a gas channel 102 having a parabolic density
profile so as to enable the formation of a laser guiding channel
for a Gaussian laser beam. As described below, the density profile
of gas channel 102--and thus the spatial profile of the laser
guiding channel formed therefrom--can also be tuned by controlling
the backing gas pressure of the gas jets.
[0024] In an ideal case, all of the gas jets will be synchronized
and set to the same gas ejection velocity, though, as described
below, in some embodiments, the gas jets can be configured to
account for variations in ejection timing and/or gas pressure to
produce a laser guiding structure in accordance with the present
invention.
[0025] The colliding neutral gas flows also create an on-axis gas
density minimum, or "gas density depression" 103 within symmetrical
gas channel 102, which is sustained for an extended duration within
the gas channel. The reason for the formation of this gas density
minimum is as follows. At the moment of the collision, the gas is
heated at the center by colliding shock waves. See I. B. Zeldovich
and I. P. Raizer, Physics of Shock Waves and High Temperature
Hydrodynamic Phenomena (Dover, N.Y., 2002) at p. 92; see also Wen
Yan, Fucheng Liu, Chaofeng Sang, and Dezhen Wang, "Two-dimensional
numerical study of two counter-propagating helium plasma jets in
air at atmospheric pressure," Physics of Plasmas 21, 063505 (2014);
and Claire Douat, Gerard Bauville, Michel Fleury, Mounir Laroussi,
and Vincent Puech, "Dynamics of colliding microplasma jets," Plasma
Sources Sci. Technol. 21, 034010 (2012). After several acoustic
times (characteristic distance divided by speed of sound) the
pressure in the high temperature region is reduced to the ambient
pressure created by the stationary gas jet flows. By this time the
shock waves are already absent, and the hot gas at the center
develops into a slowly evolving cavity with high temperature and
density contrasts between the central and peripheral parts.
Evolution of this hot cavity is described by conductive-advective
cooling that is characterized by a long lifetime and almost
constant dimensions. See D. Kaganovich, B. Meerson, A. Zigler, C.
Cohen, and J. Levin, "On the cooling of the plasma fireball
produced by a laser spark in front of liquids and solids," Phys.
Plasmas 3, 631, (1996) ("Kaganovich 1996"). Since the gas can be
considered as ideal and pressure p=nT.apprxeq.const, the gas
density n is expected to be at a minimum in the region where the
temperature T reaches its highest value.
[0026] Once the on-axis gas density depression 103 has formed by
the colliding gas flows, in accordance with the present invention,
the neutral gas is ionized, e.g., by an ionizing laser pulse or by
an electrical discharge, to generate the laser guiding structure.
Thus, in the method of the present invention, after formation of
the gas density depression, at time t1, a picosecond or nanosecond
ionizing laser pulse 104 is then focused at the entrance of the
on-axis gas density depression 103. The leading edge of laser pulse
104 ionizes the gas near the entrance to form a plasma channel 105
whose length is much longer than its transverse dimension, i.e.,
its width, such that plasma channel 105 forms a guiding structure
for a second, main laser pulse 106 fired along the central axis at
time t2. Probe beam 107 provides real-time feedback about guiding
channel parameters such as its diameter, depth, and stability. As
noted above and as described in more detail below, the geometric
arrangement of the gas jets 101a-101d and/or the backing pressure
of the gas jets can be tuned to produce a gas channel 102 having a
predetermined density profile such that gas channel 102 forms a
laser guiding structure in the form of a plasma channel that can
guide a laser pulse having predetermined spatial parameters. The
characteristics of the plasma channel 105 can be further adjusted
by tuning the parameters of the ionizing pulse.
[0027] The density profile n.sub.e(r) of gas channel 102 formed by
the collision of the neutral gas jets is
n e ( r ) .apprxeq. n e ( 0 ) + ( .DELTA. n ch r ch 2 ) r 2
##EQU00001##
where .DELTA.n.sub.ch and r.sub.ch are the depth and width,
respectively, of the channel. If the gas jets 101a-101d are
identical and are fired simultaneously, the density profile of
plasma channel 105 formed in accordance with the present invention
will be nearly parabolic, such that it can guide a main laser pulse
106 having a Gaussian laser mode and a radius
w 0 = ( .pi. r e .DELTA. n ch r ch 2 ) - 1 / 4 , ##EQU00002##
[0028] where r.sub.e is the classical electron radius. See J. P.
Palastro and T. M. Antonsen, "Interaction of an ultrashort laser
pulse and relativistic electron beam in a corrugated plasma
channel," Phys. Rev. E 80, 016409 (2009).
[0029] As described in more detail below, such a parabolic density
profile can also be produced by arranging the gas jets so that they
do not collide head-on, but instead are offset from one another. In
contrast, the gas density profiles generated by head-on collision
of the gas flows are flat in the middle at earlier times in their
evolution and become turbulent at later times.
[0030] In addition, as described in more detail below, the gas
density profile of gas channel 102 is sensitive to the backing
pressure and time jitter in the opening of the gas valves, though
as noted above the density profile of gas channel 102 can be tuned
by adjusting the backing gas pressure or the geometrical
configuration (e.g., diameters and separation) of the nozzles.
However, turbulence still tends to develop for higher pressures and
larger dimensions, where the turbulence breaks the interaction
region into several small unstable vortices, each of which is
nearly cylindrically symmetric and has close a parabolic density
profile.
[0031] The timing of the ionization can also affect the spatial
profile of the plasma channel 103 and thus the spatial profile of
the laser beam that can be guided through the channel. For example,
in the case of a plasma channel formed by gas jets having
asymmetrical gas pressures described in more detail below with
respect to FIGS. 4A and 4B, if ionization occurs at time t1=4.6
.mu.s, plasma channel 103 will have a flat density profile near the
center, making it suitable for guiding a laser pulse having a
Bessel profile fired at time t2, whereas if ionization occurs at
time t1=6 .mu.s, the channel will have a parabolic profile that can
guide a Gaussian laser pulse having a spot size w.sub.0=23 .mu.m
fired at time t2. At later times, turbulence can develop and the
channel symmetry can break, while at even later times, strong
turbulence can split the interaction region into small vortices
destroying the channel. Eventually, the center of the gas density
depression cools down and the plasma guiding channel disappears,
though as described below, the channel can be destroyed earlier
than it naturally would expire by turbulence that develops in and
around the interaction region.
[0032] As noted above, the spatial characteristics of plasma
channel 105 can be further tuned by adjusting the parameters of the
ionizing pulse.
[0033] In some embodiments, ionizing laser pulse 104 and main laser
pulse 106 share the same optical beam path with the same focusing
element. Thus, unlike other wall-less techniques mentioned above,
the "ionization while guiding" scheme of the present invention
eliminates the need of a line focus and simplifies optical
alignment.
[0034] In other embodiments, an electrode can be added near each
end of gas density structure 102 to produce an electrical discharge
which ionizes the gas to form laser guiding plasma channel 105, and
in such embodiments, pre-ionizing laser pulse 103 can be omitted.
Since the gas density is already minimal at the center and no gas
needs to be moved for the plasma channel generation, in still other
embodiments, bulk ionization of the entire gas volume is possible.
This can be done by more exotic techniques such as high pressure RF
discharge. When engineered properly, these techniques can ionize
gas in very long channels. Finally, gas can be pre-ionized by using
plasma torches instead of in the gas jets; in such embodiments, the
channel will be created by colliding plasma jets or a plasma
vortex.
[0035] An apparatus for forming a colliding jet laser guiding
structure in accordance with the present invention can use
commercial pulsed or continuous flow solenoid gas valves. In some
embodiments, slit-shaped gas nozzles can be used to extend the
length of the guiding structure so that its length is much longer
than its transverse dimensions, with the maximum channel length
being limited only by the length of the gas column and the energy
of the ionizing pulse. An elongated plasma channel can also be
achieved by stacking multiple sets of short guiding units along the
laser propagation direction, or by using custom-built long
nozzles.
[0036] In addition, to avoid density profile tapering near the ends
of the channel, two cover plates at the entrance and the exit of
the gas channel can be installed. These plates will limit the gas
from flowing in the axial direction after collision. A pinhole on
each plate can serve as the passage for the laser beam, and can
also serve as electrodes for the electrical discharge described
above, where applicable. The entire structure can be enclosed into
a large volume transparent box with differential pumping to reduce
the load on the vacuum system of the laser-plasma accelerator.
[0037] In some embodiments, more than one nozzle can be
incorporated in a single gas jet, with the nozzles being configured
so as to produce the symmetric counter-propagating gas flows having
equal angular separation around the common axis. An exemplary
configuration of such a multi-nozzle embodiment is illustrated in
FIG. 2. In the embodiment illustrated in FIG. 2, two opposing gas
jets situated 180.degree. apart are used, so that a first gas jet
201a can produce gas flows 202a and 202b and a second gas jet 201b
can produce gas flows 202c and 202d, gas flows 202a, 202b, 202c,
and 202d, with the gas jets in each nozzle being oriented
90.degree. from the other so that the four gas flows are
symmetrically oriented around central axis 203. Such a
configuration simplifies the resolution of the time jitter issues
described below by reducing the number of gas jets from four to
only two, easing overall synchronization control.
[0038] Additional aspects of colliding gas jet flows and formation
of a laser guiding channels from such colliding gas flows are
described below.
[0039] In order to examine the evolution of the colliding gas jet
flows and laser guiding channels from an apparatus and method in
accordance with the present invention, the inventors used a 2-D
version of the 3-D SPARC computer simulation software described in
detail in D. Kaganovich, D. F. Gordon, M. H. Helle, and A. Ting,
"Shaping gas jet plasma density profile by laser generated shock
waves," Journal of Applied Physics 116, 013304 (2014) ("Kaganovich
2014"). FIGS. 3A-3C, 4A-4B, 5A-5B, 6A-6B, and 7A-7B illustrate the
results from these simulations and illustrate aspects of the ways
in which a plasma channel/laser guiding structure can be created by
the use of symmetrically oriented counter-propagating gas flows in
accordance with the present invention.
[0040] A screen shot of a SPARC-simulated generic gas jet
configuration is illustrated in FIG. 3A. All simulations were
conducted for helium gas, motivated by its widespread use in LWFA
experiments, with dimensionless specific heat at constant volume
cv=3/2, thermometric conductivity K=1.7 cm.sup.2/s, and kinematic
viscosity v=1.2 cm.sup.2/s.
[0041] The initial reservoir pressure was set to 2 atmospheres. The
nozzles had an internal thickness of 250 orifice orthogonal
distance of 1 mm, and length of 0.65 mm. The thickness of all walls
was 50 .mu.m. The corresponding Reynolds number for these
parameters is estimated to be Re=vL/v.apprxeq.2500, where
v.apprxeq.3000 m/s is the maximum escape velocity of helium into
vacuum, see Zeldovich, supra, and L.apprxeq.100 .mu.m is the
characteristic length for the region of interest.
[0042] At time t=0, the reservoirs are uniformly filled with room
temperature gas at a backing pressure of 2 atmospheres. The gas
then starts to freely expand through the 0.25 mm thick nozzles into
vacuum. As can be seen in FIG. 3A, a gas density depression
surrounded by higher density gaseous wall forms when the gas flows
encounter each other near the center. After about 4 .mu.s, the gas
density reaches a minimum around the center of the collision
creating a channel in the neutral gas.
[0043] When ionized as described above, e.g., by an ionizing laser
pulse or electrical discharge fired through the center thereof at
time t1, this gas density depression region can serve as a guiding
channel, e.g., for a subsequent laser pulse, where the
radially-symmetric, parabolic electron plasma distribution permits
a laser beam having a Gaussian radial profile to be guided through
the channel without its size being changed. See G. M. Mourou, T.
Tajima, and S. Bulanov, "Optics in the relativistic regime," Rev.
Mod. Phys. 78, 309 (2006). The gas pressure and geometrical
parameters of the simulation were chosen to reduce the Reynolds
number and to avoid turbulence as long as possible while keeping
the channel deep enough for laser guiding.
[0044] FIG. 3B shows is a color map of the gas temperature and
shows the time evolution of the temperature along a horizontal line
that crosses the center of the gas density depression. The
temperature in the center remains high for about 2 .mu.s, exceeding
800 K at earlier times, cooling from 800 K as time progresses from
t=2 .mu.s to about 300 K at t=16 .mu.s, with the channel diameter
narrowing around the center from about 1 mm at t=2 .mu.s to about
0.5 mm at t=16 .mu.s.
[0045] The flat-top temperature profile across the gas channel and
slow change in the channel diameter as the temperature rises shown
in FIG. 3B are typical signatures of conductive-advective cooling.
See Kaganovich 1996, supra. During this process, the thermal energy
in the middle is transferred to the colder in-flowing gas. This gas
inflow from the periphery is necessary to maintain approximately
constant pressure across the interaction region. As a result, the
size of the hot area remains the same, while high temperature and
low density contrasts are preserved between the center and
surrounding areas.
[0046] The plots in FIG. 3C are the linear representations of the
gas density color map shown in
[0047] FIG. 3A, where plot 301 is a horizontal lineout showing the
variation in gas density measured from the center of the gas flows
at time t=4.6 .mu.s and plot 302 is a lineout showing the variation
in gas density along a 45.degree. line extending through the center
of the gas flows at the same time t=4.6 .mu.s.
[0048] As can be seen from the plots 301 and 302, these lineouts
overlap near the center, showing that the intersecting gases in
this exemplary case produce a cylindrical rather than a parabolic
gas density profile, with the density profile resembling a
stepped-index fiber supporting Bessel function laser propagation
modes. See Ajoy Ghatak and K. Thyagarajan, An Introduction to Fiber
Optics, (Cambridge University Press, 1998), pp. 149-151.
[0049] The plots in FIGS. 3A-3C depict an idealized gas flow, where
the gas jets were configured symmetrically with equal reservoir
backing pressure and synchronized valve release. In a real system,
however, deviations, such as unequal backing pressures and time
jitters, may be present. To estimate the requirements of a
practical device, the inventors of the present invention performed
additional simulations with intentional gas jet asymmetries.
[0050] The inventors first investigated the formation of the
density depression with slightly different reservoir backing
pressures. In an exemplary case described herein, the backing
pressure in one of the jets was offset by 1% and in another by 2%,
such that two of the jets had backing pressures of 2.00 atm, while
the other two had backing pressures of 2.02 and 2.04 atm,
respectively.
[0051] The results are shown in FIGS. 4A and 4B. As can be seen
from the screen shot shown in FIG. 4A, a gas density minimum that
can be used to form the laser guiding plasma channel is still
formed by the collision of the gas flows having unequal pressure,
though the location of the minimum is shifted slightly up and to
the right as a result of the higher gas pressures in the two gas
jets.
[0052] As can be seen from the lineout plots in FIG. 4B, while the
location of the gas density minimum shifts off-center as described
above, the gas density profiles also change with time, and so, by
ionizing the gas at different times, channels suitable for
different types of laser pulses can be created. Thus, horizontal
lineout 401, which shows the gas density profile at time t=4.6
.mu.s, is flat at its center, which, as described above is suitable
for the formation of a guiding channel for a laser pulse having a
Bessel profile. In contrast, horizontal lineout 402, which shows
the gas density profile at t=6.0 .mu.s, has a substantially
parabolic density profile (compare to parabolic fit plot 403),
making it suitable for the formation of a guiding channel for a
Gaussian laser pulse, e.g., a pulse having a radius w.sub.0=23
.mu.m as shown in the FIGURE.
[0053] However, in both cases, off-center shift of the gas density
minimum increases significantly for even-larger pressure
differences. In addition, the lifetime of such asymmetric channels
is shorter since it is prone to the earlier development of
turbulence. See Glasner, supra. Thus, care should be taken to
minimize the pressure differences in the gas jets so as to maximize
the utility of the guiding channel to be formed therefrom.
[0054] Another practical consideration that could affect the
guiding structure is time jitter in the gas jet valve openings. In
the simulations described above, the gas in all of the gas jets was
deemed to be released simultaneously at time t=0 by instantaneously
opening the valves. However, real gas jets have opening times
ranging from a few microseconds for piezo-driven valves to a few
hundred microseconds for solenoid-based ones, and so simultaneous
opening is not likely to occur. While slowly opening the jets might
relax the requirements for synchronized gas flow, offsetting the
opening times too much, either intentionally or inadvertently, can
result in the creation of an unstable gas density depression at the
vortex of the colliding gas flows.
[0055] FIGS. 5A and 5B illustrate the effects of such time-offset
opening of the gas jets on creation of a plasma guiding channel by
the method of the present invention.
[0056] In the simulation illustrated by the screen shot shown in
FIG. 5A, two of the jets were opened 5 microseconds later than the
other two. As can be seen in FIG. 5A, collision of the gas jets
still creates a vortex with a minimum density spot traveling around
the central axis.
[0057] However, as can be seen from the lineout plots shown in FIG.
5B, the gas density minimum measured along a horizontal direction,
shown by horizontal lineout 501, is in a different place along the
x axis than is the gas density minimum measured along a vertical
direction, as shown by vertical lineout 502. While both the
horizontal and vertical density profiles are essentially parabolic
(see parabolic fit 503), suitable for formation of a guiding
channel for a Gaussian laser pulse having a radius w.sub.0=25 the
location of that channel will constantly change over time, making
alignment of the laser pulse into such a "wobbly" channel
difficult. Fortunately, gas jets with shorter jitter times (<3
.mu.s) can generate stable channels similar to those generated by
symmetrical gas jets, so care should be taken to minimize such time
delays.
[0058] In some cases, gas channels formed by jets having a longer
time jitter can be transformed into more stable guiding structure
by introducing a longitudinal gas flow, e.g., by a pump configured
to move the gas along the channel and/or by tilting the gas nozzles
in the direction of the z-axis (i.e., in a direction perpendicular
to the x-y plane of FIG. 5A). When a longitudinal gas flow is
introduced, the gas will experience a spiraling motion, creating a
more stable and stationary vortex and thus a more stable and
stationary gas density minimum. See J. Jeong and F. Hussain, "On
the identification of a vortex," Journal of Fluid Mechanics 285:
69-94 (1995).
[0059] In other embodiments, a more stable and controllable gas
vortex can be achieved by arranging the gas jets so that, while
still symmetric around the central axis, they are offset one from
another.
[0060] In an exemplary simulation of this embodiment of an
apparatus for forming a laser-guiding plasma channel in accordance
with the present invention, each nozzle is shifted laterally by 350
.mu.m so that opposing gas jets do not collide head-on, but instead
are directed so that they travel in opposite but parallel
directions.
[0061] A screen shot from the SPARC simulation of this embodiment
is shown in FIG. 6A and shows the evolution of the vortex gas
density profile in such a case. Although small revolutions of the
gas density depression around the center still present a potential
problem for laser alignment, mode oscillation studies indicate that
a small misalignment would still guide the laser pulse through the
channel with small centroid oscillations. See P. Sprangle, J.
Krall, and E. Esarey, "Hose-Modulation Instability of Laser Pulses
in Plasmas," Phys. Rev. Lett. 73, 3544 (1994); and A. J. Gonsalves,
K. Nakamura, C. Lin, J. Osterhoff, S. Shiraishi, C. B. Schroeder,
C. G. R. Geddes, C s. Toth, E. Esarey, and W. P. Leemans, "Plasma
channel diagnostic based on laser centroid oscillations," Physics
of Plasmas 17, 056706 (2010). The channel stability can be further
improved by adjusting the geometrical configuration of the nozzles,
which will be studied in more detail in the future.
[0062] The lineout plots shown in FIG. 6B illustrate the benefits
of forming a gas channel using offset gas jets in accordance with
this embodiment of the present invention. As can be seen in FIG.
6B, both the horizontal lineout 601 and the 45.degree. diagonal
lineout 602 show a gas density profile having a nearly parabolic
shape (compare parabolic fit 603) similar to that shown by
horizontal lineout 301 for four identical equal gas flows, and so
is very suitable for the formation of a guiding channel for a
Gaussian laser pulse, e.g., one having a radius w.sub.0=25 .mu.m as
shown in the FIGURE.
[0063] In addition, combining the offset colliding gas flows with a
longitudinal motion of the gas as described above can further
provide stability and tunability to the gas channel. See K.
Duraisamy and S. K. Lele, "Evolution of isolated turbulent trailing
vortices," Phys. Fluids 20, 035102 (2008).
[0064] Thus, the present invention provides a technique for
producing a guiding channel for a laser pulse. No other currently
known technique can produce a guiding channel from neutral gas as
is produced by the method of the present invention. The technique
of the present invention does not require any additional optical
components and the length of the guiding structure is limited only
by the length of the gas column. The device can be used at high
repetition rates that depend only on the vacuum pumping efficiency.
The wall-free technique allows use of standard diagnostic technique
such as optical interferometry, and is compatible with electron
injection schemes with transversely incident laser pulses. See M.
Chen, E. Esarey. C. G. R. Geddes, E. Cormier-Michel, C. B.
Schroeder, S. S. Buianov, C. Benedetti, L. L. Yu, S. Rykovanov, D.
L. Bruhwiler, and W. P. Leemans, "Electron injection and emittance
control by transverse colliding pulses in a laser-plasma
accelerator," Phys. Rev. STAB 17, 051303 (2014); and R. Lehe, A. F.
Lifschitz, X. Davoine, C. Thaury, and V. Malka, "Optical Transverse
Injection in Laser-Plasma Acceleration," Phys. Rev. Lett. 111,
085005 (2013).
[0065] In contrast to capillary based plasma channels, the
colliding jets scheme is compatible with standard transverse plasma
diagnostics and cannot be damaged by a laser pulse. Enclosure of
the gas jets assembly into a transparent container with pinholes
for the main laser beam can reduce requirements to a differential
vacuum pumping and increase the repetition rate.
[0066] In addition, the colliding jets plasma guiding structure
formed in accordance with the present invention is scalable and
tunable to a wide range of plasma parameters. An exemplary case of
this is illustrated by the plots in FIG. 7B, which provide lineouts
for the offset gas jets shown in FIG. 7A (same as in FIG. 6B) at
different gas pressures, and shows that in the case of offset gas
jets, higher gas pressures produce more stable, parabolic gas
density profiles. Thus, as shown in FIG. 7B, gas jets having a
backing pressure of 2.0 atm inside the gas jet reservoirs (lineout
701) produce an ill-defined density profile, where the density
varies considerably over the horizontal distance from the center
and has no readily defined minimum. Gas jets having a backing
pressure of 4.0 atm (lineout 702) produce an improved gas density
profile having a roughly parabolic shape, while the gas jets having
a backing pressure of 8.0 atm (lineout 703) produce an almost fully
parabolic density profile, suitable, as described above, for
creation of a channel to guide a Gaussian laser pulse.
[0067] Thus, in accordance with this aspect of the present
invention, simply by changing the gas pressure, we can change depth
of the plasma channel and, as a result, change the matching radius
of the laser beam, which allows us to focus the laser beam in
different ways while still being able to guide it through the
channel.
[0068] In other embodiments, the plasma guiding channel can be
configured to guide a laser beam having a specified spot size by
adjusting the nozzle separation distances, which changes the
diameter of the channel. Other parameters which can be varied to
obtain a channel configured to guide a desired laser beam include
the offset, the tilt, and/or the shape of the gas nozzles.
[0069] As described above, gas ionization to form the plasma
guiding channel can be performed by standard techniques like laser
or electrical discharge. For example, for a shorter channel, a
picosecond or nanosecond laser pulse focused at the entrance or
along the gas channel can ionize the gas as shown in FIG. 1, while
a longer channel can be formed using an electrical discharge to
ionize the gas in and around the center and create the required
plasma density distribution.
[0070] Since the gas density is already minimal at the center and
no gas needs to be moved for the plasma channel generation, in
still other embodiments, bulk ionization of the entire gas volume
is acceptable. This can be done by more exotic methods like high
pressure RF discharge. See Claire Tendero, Christelle Tixier,
Pascal Tristant, Jean Desmaison, and Philippe Leprince,
"Atmospheric pressure plasmas: A review," Spectrochimica Acta Part
B, 61, 2 (2006). As an advantage over laser ionization, these
techniques can be engineered to ionize gas over longer
distances.
[0071] In still other embodiments, the gas jets can be replaced by
high density plasma torches. See Andreas Schutze, James Y. Jeong,
Steven E. Babayan, Jaeyoung Park, Gary S. Selwyn, and Robert F.
Hicks, "The Atmospheric-Pressure Plasma Jet: A Review and
Comparison to Other Plasma Sources," IEEE Trans. Plasma Sci., 26,
1685,(1998). In such cases, the ionized channel can be created by
colliding plasma jets or plasma vortices.
[0072] Alternatives
[0073] There are alternative techniques for the formation of a
laser guiding structure.
[0074] One alternative to the colliding jets technique of the
present invention utilizes the hydrodynamic radial expansion of the
plasma heated by high energy laser pulse. In such a technique,
however, in order to produce axially extended guiding channel, the
"hydrodynamic heater" pulses must be line-focused into the gas
column, either by an axicon (conical lens) or by cylindrical
focusing optics, see C. G. R. Geddes et al., "High-quality electron
beams from a laser wakefield accelerator using plasma-channel
guiding," Nature 431, 538 (2004), which introduces significant
complexity into the optical alignment of the lasers. In such cases,
the heater beam size and the clear aperture of the line-focusing
element further impose limits to the maximum channel length.
[0075] In another alternative to the method of the present
invention, a pre-formed guiding device is a discharge-based
dielectric capillary. However, in this case, the dielectric wall is
subject to damages by the laser field, discharge current, and
plasma. In addition, standard diagnostic techniques such as optical
interferometry are no longer valid for transversely probing the
plasma density profile in the capillary, making it more difficult
to monitor the performance of the waveguide.
[0076] However, none of these alternative techniques can produce a
predetermined density profile from neutral gas as can method of the
present invention.
[0077] Thus, the present invention provides an apparatus and method
for creating a free-space plasma channel for guidance of
high-intensity laser beams. The gas outflow of gas jets
symmetrically arranged around a central axis collides at their
center and forms a vortex structure comprising a gas channel having
a parabolic density profile in which an on-axis gas density
depression is surrounded by higher density walls. The gas channel
can be ionized, either by a laser pulse or by an electrical
discharge, to create a plasma channel that can guide an ultrashort
laser pulses for laser-based particle acceleration and related
applications. A detailed 2-D fluid dynamics simulation of this
free-space guiding channel indicates generation of a stable guiding
profile lasting tens of microseconds. Analysis has shown showed
that a 1% tolerance in the backing pressures and/or a few
microseconds in time jitter are acceptable for the practical
application of the device.
[0078] Although particular embodiments, aspects, and features have
been described and illustrated, it should be noted that the
invention described herein is not limited to only those
embodiments, aspects, and features, and it will be readily
appreciated by those skilled in the art that modifications to such
embodiments, aspects, and features may be made. The present
application contemplates any and all modifications within the
spirit and scope of the underlying invention described and claimed
herein, and all such modifications and embodiments are within the
scope and spirit of the present disclosure.
* * * * *