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Studying astrophysical collisionless shocks with counterstreaming plasmas from high power lasers
High Energy Density Physics 8 (2012) 38e45
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High Energy Density Physics journal homepage: www.elsevier.com/locate/hedp
Studying astrophysical collisionless shocks with counterstreaming plasmas from high power lasers Hye-Sook Park a, *, D.D. Ryutov a, J.S. Ross a, N.L. Kugland a, S.H. Glenzer a, C. Plechaty a, S.M. Pollaine a, B.A. Remington a, A. Spitkovsky b, L. Gargate b, G. Gregori c, A. Bell c, C. Murphy c, Y. Sakawa d, Y. Kuramitsu d, T. Morita d, H. Takabe d, D.H. Froula e, G. Fiksel e, F. Miniati f, M. Koenig g, A. Ravasio g, A. Pelka g, E. Liang h, N. Woolsey i, C.C. Kuranz j, R.P. Drake j, M.J. Grosskopf j a
Lawrence Livermore National Lab, 7000 East Ave., Livermore, CA 94550, USA Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA c University of Oxford, Oxford, UK d Osaka University, Osaka, Japan e Laboratory for Laser Energetics, Rochester, NY, USA f ETH Science and Technology University, Zurich, Switzerland g Ecole Polytechnique, Paris, France h Rice University, Houston, TX, USA i University of York, Heslington, York, UK j University of Michigan, Ann Arbor, MI, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 November 2011 Accepted 1 November 2011 Available online 9 November 2011
Collisions of high Mach number flows occur frequently in astrophysics, and the resulting shock waves are responsible for the properties of many astrophysical phenomena, such as supernova remnants, Gamma Ray Bursts and jets from Active Galactic Nuclei. Because of the low density of astrophysical plasmas, the mean free path due to Coulomb collisions is typically very large. Therefore, most shock waves in astrophysics are “collisionless”, since they form due to plasma instabilities and self-generated magnetic fields. Laboratory experiments at the laser facilities can achieve the conditions necessary for the formation of collisionless shocks, and will provide a unique avenue for studying the nonlinear physics of collisionless shock waves. We are performing a series of experiments at the Omega and Omega-EP lasers, in Rochester, NY, with the goal of generating collisionless shock conditions by the collision of two highspeed plasma flows resulting from laser ablation of solid targets using w1016 W/cm2 laser irradiation. The experiments will aim to answer several questions of relevance to collisionless shock physics: the importance of the electromagnetic filamentation (Weibel) instabilities in shock formation, the selfgeneration of magnetic fields in shocks, the influence of external magnetic fields on shock formation, and the signatures of particle acceleration in shocks. Our first experiments using Thomson scattering diagnostics studied the plasma state from a single foil and from double foils whose flows collide “headon”. Our data showed that the flow velocity and electron density were 108 cm/s and 1019 cm3, respectively, where the Coulomb mean free path is much larger than the size of the interaction region. Simulations of our experimental conditions show that weak Weibel mediated current filamentation and magnetic field generation were likely starting to occur. This paper presents the results from these first Omega experiments. Published by Elsevier Ltd.
Keywords: Astrophysical Collisionless shocks Weibel instability Electromagnetic instabilities Interpenetrating plasmas Thomson scattering
1. Introduction Shock waves traveling >3000 km/s are observed in supernova remnants, such as in SN1006 [1]. Space and ground-based telescopes * Corresponding author. Tel.: þ1 925 422 7062; fax: þ1 925 423 6319. E-mail address: [email protected] (H.-S. Park). 1574-1818/$ e see front matter Published by Elsevier Ltd. doi:10.1016/j.hedp.2011.11.001
study astrophysical collisionless shocks observationally at many different wavelengths. As an example, Fig. 1 shows Chandra x-ray satellite observations of SN1006 in two different x-ray bands [2]. From these observations we can compare the shock thickness with the average Coulomb mean free path. The typical temperature and density behind the shock front is Ti w 15 keV (Te w 0.5e1 keV) and ni w 1 cm3. The corresponding proton Coulomb mean free path
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Fig. 1. (a) Profiles of the filaments in the SN 1006 northeast shell. Upper panels show the profiles in the (2.0e10.0 keV) band, whereas the lower panels in the (0.4e0.8 keV) band with the best-fit models (solid lines). The dashed lines in the lower panels represent nonthermal photons extrapolated from the hard band flux of the power law (upper panels). The dotted lines are the thermal component after subtracting the nonthermal contamination (dashed lines). Upstream is to the left and downstream is to the right. (b) Two-color images of SN 1006 northeast shell binned with 100 scale. Red and blue are 0.5e2.0 keV and 2.0e10.0 keV, respectively, both in logarithmic scale. [Reproduced from Bamba, ApJ, 2003]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
length is estimated to be 13 pc (¼4 1019 cm). The diameter of the entire SN1006 remnant is about 10 pc (¼3 1019 cm). The shock front width is about 0.04 pc (¼1.2 1017 cm). With these numbers, one concludes that the thickness of the shock front for SN1006 SNR is less than 1% of the radius and the Coulomb mean free path is 400 times longer than the shock front thickness, namely, the shock is collisionless [3]. Astrophysical shocks span a wide range of shock speeds, Mach numbers, magnetizations, and can occur in plasmas of varying composition, such as electron-ion or electron-positron plasmas. Despite their diversity, collisionless shocks share common characteristics: they are inferred to efficiently accelerate nonthermal particles and to generate and amplify magnetic fields, in addition to being able to effectively decelerate supersonic flows. As a result of the nonlinear plasma processes involved in the shock formation, the physics of such shocks remains unclear, and the conditions for efficient particle acceleration are not fully understood. It has been recently proposed [4,5,6,7] that the generation of magnetic fields can occur in these cosmic shocks on a cosmologically fast timescale via the Weibel (or filamentation) instability [8]. 3D particle-in-cell (PIC) numerical simulations have confirmed that the strength and scale of Weibel-generated magnetic fields are consistent with what would be required to play a dominant role in the magnetization of astrophysical collisionless shocks [9,10,11]. PIC simulations show how Weibel instabilities produce a magnetic field that mediates the formation of a shock at the interaction of unmagnetized plasma flows [12]. In Fig. 2(a), density filaments characteristic of the Weibel instability and the shock thus formed are visible, while Fig. 2(b) shows the density and the magnetic energy density in the shock region. The role of collisionless shocks is particularly important to the origin of ultrahigh energy cosmic rays (UHECR). While there is evidence that cosmic rays are primarily produced via first order Fermi acceleration at astrophysical shocks [13,14,15], the acceleration up to the knee, i.e., up to energies of 1015 eV, has challenged theorists for a long time. Recently, Bell [16] has proposed a novel mechanism for the amplification of magnetic fields by nonresonant interaction of cosmic ray driven currents with a preexisting magnetic field at the shock front. In this scenario, as the magnetic field changes the dynamics of shock acceleration, the maximum energy of the accelerated particles is amplified by orders of magnitude.
In astrophysical plasmas, there is no way to directly measure the key quantities to investigate the shock dynamics and particle acceleration by collisionless shocks. Our proposed investigations will address the underlying physics of collisionless shock formation via scaled laser experiments. Analytic estimates indicate that scaling from astrophysical scales to laboratory experiments at the Omega and Omega-EP lasers should be possible. 1.1. Laboratory collisionless shock experimental consideration The geometry of the experimental configuration is shown in Fig. 3. Two high velocity plasma flows are generated by ablation from two planar targets oriented to intersect at some point in between. We want to satisfy two conditions: 1. The collision mean free path lmfp for the more massive ion component (carbon, in the case of CH plasmas) should be much larger than the system size (that is, the spatial scale of the interacting flows, [int ): lmfp >> [int . 2. The system size, [int , must be much larger than the scale, [* , needed to generate plasma instabilities: [int >> [* . So, we are looking for the conditions where
[* [int lmfp
(1)
Fig. 3 illustrates the geometry: this figure corresponds to a limiting case where the flows interpenetrate with each other. If, however, the interaction (collisionless or collisional) is strong, then strong shocks are formed in the intersection region, flow velocity decreases, and the plasma is heated. For example, for CH flows with a velocity of 108 cm/s intersecting at an angle of a ¼ 45 , heating to a temperature of Ti w 3e5 keV is predicted to occur in a collisionless shock (see discussion of Fig. 9). This could be detected by a variety of techniques. In particular, one flow made of CH interacting with another flow of CD will produce neutrons according to the strength of their interaction. Since the temperature of a noninteracting flow is relatively low, DD (nuclear) reactions in the isolated CD flow will be weak. They will be weak also in the case where two flows pass through each other without interaction. Conversely, if the interaction is strong, e.g., a collisionless shock is formed, deuterium will be heated to a high temperature, and
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Fig. 2. (a) Filamentary density structure in an unmagnetized shock mediated by the Weibel instability as simulated by a 3D PIC code [Reproduced from Spitkovsky, AIP 2005]. Color represents density: yellow corresponds to high, green to intermediate, and black to low density. The green striations are density filaments caused by the Weibel instability, and are a precursor to collisionless shock formation. The increase in density (transition from green to yellow) indicates the formation of a shock. The incoming flow propagates from the lower left to the upper right, and the shock moves to the lower left; (b) Density structure through the unmagnetized shock (solid line, left axis) and magnetic energy normalized by the upstream kinetic energy (thin line, right axis). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
a measureable burst of DD-produced neutrons should occur at the intersection time. When evaluating lmfp, we assume that the temperature of the colliding flows is much smaller than the ion energy due to the bulk flow velocity; this is consistent with LASNEX radiationhydrodynamics simulations. In this case, the numerical estimate for lmfp can be presented as:
lmfp ðcmÞw5
A2 1013 4Z Z
a ½vðcm=sÞ cos4 2 nz cm3 4
(2)
where AZ, Z, and nZ are the atomic weight, charge, and number density of the main ion component, and v is the flow bulk velocity before the collision with the other flow. This equation is based on Eq. (14.12) of Ref. [17], with the Coulomb logarithm assumed to be 10. The cos(a/2) factor is related to the center-of-mass effect. A numerical example is helpful: for v ¼ 108 cm/s, Az ¼ 12, Z ¼ 6, nZ¼1018 cm3, and a ¼ p/2, one finds lmfpw1.5 cm. Evaluating [* is a formidable task; present-day computer codes and computing power are still not up to this task. This makes the proposed experiment all the more interesting and adds importance to the whole endeavor. A possible heuristic model (based on the growthrate assessments similar to those presented in Ref. [18]) for evaluating [*ES for electrostatic plasma instabilities can be presented as
[*ES wK
v W upi Te
(3)
where K >> 1 is a numerical factor accounting for the number of the growth times required for the instability to reach a developed stage, W is the kinetic energy of the main ion component in the flow, Te is the electron temperature (in energy units) in the flow prior to the collision, v is the bulk flow velocity, and upi is the ion plasma frequency. Note, v/upi is roughly the distance traveled by the flow in one ion plasma wave oscillation period. Hence, K >> 1 implies that the plasma in the interaction region should correspond
Fig. 3. The geometry of the proposed experiment. The condition for collisionless shock creation is: [* [int lmfp where [* is the plasma interaction length threshold for triggering plasma instabilities.
to many (>>1) plasma waves. Numerically inserting characteristic values gives:
WðeVÞ ¼ 5:2 1013 Az ½vðcm=sÞ2 For
[*ES,
(4)
the numerical estimate is:
pffiffiffiffiffiffi
vðcm=sÞ AZ [*ES ðcmÞw103 K qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z nz cm3
WðeVÞ Te ðeVÞ
(5)
For K ¼ 30, v ¼ 108 cm/s, Az ¼ 12, Z ¼ 6, nZ¼1018 cm3, and Te ¼ 600 eV, the length [*ES is 0.18 cm. If one takes the estimate in Eq. (5) compared to Eq. (2) at face value, the optimum conditions for the study of collisionless shocks favor higher flow energies and electron temperatures, and lower flow densities, limited of course by diagnostic sensitivities and constraints. Lower-Z materials are somewhat preferable as lmfp very rapidly increases for lower-Z. Estimates from Eqs. (3) and (5) correspond to that for an electrostatic instability, which will probably be dominant at the initial stage of interaction. For the electromagnetic instability, [*EM , of the Weibel type, the estimate corresponding to Eq. (3) would be
[*EM wK
c
upi
; where K>1
(6)
Here, c/upi corresponds to ion plasma skin depth, namely, the distance light could travel in one ion plasma wave oscillation period. For the characteristic parameters mentioned above, estimates from Eqs. (3) and (6) yield the same or of magnitude results. Of course, one has to interpret these estimates with care, as there is no widely accepted nonlinear theory for the problem with which we are concerned. In this regard, our experiment will guide the theory and simulations. One of the concerns for the proposed experiment is the possible presence of a regular magnetic field, generated in the course of the flow formation at the targets. This field could then be advected with the flow. The collision of two flows with embedded magnetic fields could produce a big splash (literally and figuratively), even if there are no micro-instabilities present. This may be an effect that is very interesting in its own right. If a magnetic field is generated by the Vne VTe, “fountain field” mechanism, it will be predominantly azimuthal. The axial current driven by the laser-ablated plasma would flow outwards normal to the target near the axis and in the opposite direction at larger radii, somewhat like a current “fountain”, closing radially near the flow end. This field will have a relatively minor effect on the interpenetration of the ions if the ion gyro-radius in the field is significantly larger than [*EM . The gyro-radius can be evaluated as:
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Fig. 4. The Dec 2010 Omega experimental geometry for the (a) single and (b) double foil cases. The laser intensity on the target was 8 1015 W/cm2.
pffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi AZ WðeVÞ Z BðkGÞ
ri ðcmÞw0:15
(7)
Introducing the plasma b, the ratio of the plasma particle pressure to the magnetic pressure, one can write: 9
BðkGÞw6 10
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ne cm3 Te ðeVÞ
b
(8)
For ne ¼ 1019, and Te ¼ 103 eV, one has B(kG) w 600/Ob. For b w 100, B w 60 kG, and the ion gyro-radius (for carbon ions with
the energy of 60 keV), according to Eq. (6), is w0.4 cm. This shows that the flows have to be characterized individually with respect to the regular magnetic field. The effect of the regular field will be present for the head-on collisions of flows (a ¼ 0). The magnetic field that would affect the interpenetration of the electrons of the two flows will be much weaker than that required to affect the ions, as the electron gyro-radius is much smaller than the ion gyroradius. However, the inhibition of mixing of electrons of the two flows may not have too strong an effect on the interpenetration of the ions, provided the directed ion energy is much higher than their pre-collision thermal energy.
The basic requirements for creating a collisionless shock in the laboratory are that ([*ES , [*EM ) << [int << lmfp: namely, the shock thickness [* determined by electrostatic or electromagnetic (Weibel) instabilities needs to be smaller than spatial scale of the interacting plasmas (the experimental scale), and these lengths should be much less than the Coulomb mean free path length. We report our first experiment to study the plasma condition generated by counterstreaming plasmas. The plasma temperature, density and the flow velocities were measured by Thomson Scattering using a 0.53 mm probe laser on Omega. 2. Experimental results Our first Omega experiment concentrated on measuring and understanding the plasma conditions that are created by the Omega lasers on single and double foil configurations. Thomson scattering was used to characterize the plasma created by 10 heater-drive beams incident on a CH foil. All our 12 shots produced high quality data with 2 different laser intensities, 3 different probe times, in single and double foil geometry. The heater-drive beams deliver 5 kJ of energy in a 1 ns square pulse shape. The target geometry is shown in Fig. 4. A probe beam of 0.53 mm wavelength
Fig. 5. An example of Thomson scattering data and the fit for a single foil shot. (a) ion features; (b) electron features; (c) ion features data and fit; (c) electron features data and fit. A time slice of the ion and electron features are simultaneously fit to produce Te, Ti, ne, vflow, udrift parameters.
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Fig. 6. Data from double foil shows much higher ion temperature and higher electron density indicating stagnation of the plasmas. The flow velocity is also reduced systematically for the double foil flows.
Fig. 7. Measured plasma parameters from a single foil flow compared with a 2-D hydrodynamics simulation. The measured electron temperature is high compared to that simulated, which may be due to the probe beam heating. Blue points are single foil data with laser intensities of 8 1015 W/cm2; green are single foil data with laser intensities of 8 1014 W/cm2; red are double foil data with 8 1015 W/cm2 on each foil; the black line is the 2-D LASNEX simulation for the single foil with 8 1015 W/cm2. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 8. 2-D radiation-hydrodynamics simulations from LASNEX at 4 mm distance from the target: (a) velocity, ne, ni, Te, Ti, vflow as function of time; (b) Collision mean free path (black) and characteristic electrostatic instability (red) and ion skin depth, c/upi (blue-dotted). The electromagnetic instability length is 10e300 of ion skin depth (drawn in this figure is 300 c/upi.) for collisionless shocks, [*ES or EM < lmpf condition is required. (c) 2-D LASNEX simulations show the distribution of electron density (left) and azimuthal magnetic field (right) in r-z space at 2 different times. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
(labeled “2u probe” in the figures) is pointed 4 mm from the foil surface. The Thomson-scattered (TS) light of the 2u probe laser in the plasma is collected with an f/10 optic on a Ten Inch Manipulator in TIM-6 at a distance of 50 cm from the plasma. Detailed description of this instrument can be found in Ref. [19]. The Thomson scattering probe volume was 100 mm 100 mm 60 mm defined by the optical magnification and the overlap of the streak camera slit (100 mm) and the spectrometer slit (100 mm), in the plasma with the probe beam, which was focused to 60 mm diameter. We chose the target axis such that the k-vector is normal to the target normal measuring the plasma condition along the plasma flow direction. In our current set-up, the Thomson scattering observes the projection of the velocity along the ion-acoustic wave k-vector. Thomson scattering was measured from the electron feature (collective scattering from electron-plasma waves) and the ion feature (collective scattering from ion-acoustic waves). An example of electron and ion features from a single foil shot is shown in the top panel of Fig. 5. Our data set includes temporal measurements from 2.0 to 3.0 ns, 5.0e6.0 ns, and 7.8e8.8 ns. Time-slices of the data from the electron feature are then fit with the Thomson scattering form factor that allows a measurement of the electron temperature (Te) and electron density (ne) [20]. With constraints from the electron feature fit, the ion feature can then be used to measure the ion temperature (Ti) and bulk plasma flow velocity (vflow). This can be understood from the simplified dispersion rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4lprobe ZTe 3Ti sinðq=2Þ þ . An example of fitting relation, Dl ¼ c M M the results is shown in the bottom panel of Fig. 5. The double foil data also showed very interesting results. The difference between the single foil and the double foil data for the ion feature is striking, as shown in the left panel of Fig. 6. A similar
fitting procedure was applied to the double foil data set. Fig. 6 shows the results at 8.6 ns after the laser pulse. Compared to the single foil flow, the ion temperature and electron density are considerably higher. Another observation is that the flow velocity is reduced for all the double foil flows indicating interaction between the two flows at late in time. The measured plasma characteristics from different shots covering a 2e9 ns time interval and single and double foils are compiled in Fig. 7, where the flow velocity, electron density, ion temperature and electron temperature are shown. Different color data points represent different experimental conditions of single foil shots (blue), double foil shots (red), and single foil with 10 times lower drive laser intensity (green). The data is compared to 2D LASNEX [21] hydrodynamic simulations, indicated by the solid black curves. There is good agreement between the measured and simulated bulk plasma flow velocity over all three time intervals. The measured electron density shows a sharp increase between 5.0 and 6.0 ns, which is also present in the simulations, indicating that the bulk of plasma arrives at this time. This is consistent with flow arrival at the 4 mm location of the plasma flow with velocity of w103 km/s. The measured electron temperature is significantly higher than the simulations. We attribute this to reheating the plasma by the TS probe beam. The measured ion temperature is consistent with the 2D simulations. An electron temperature of 170 eV had to be assumed during this time interval due to a lack of electron feature data. 3. Discussion In order to see whether our experimental results meet the requirements for creating a collisionless shock, we examine the 2-D LASNEX simulation of a single foil for the plasma conditions of our
Fig. 9. PIC simulations of electron and ion distribution functions when the shock is just beginning to form (left panel) compared to when the shock is fully formed (right panel). Note the asymmetry of the ion velocity distribution (b) versus symmetry (d) depending on the shock-forming stage. This signature can be utilized to identify the time when the shock is fully forming.
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Fig. 10. PIC simulation of shock creation using the measured plasma condition from our experiment (left panel) and fully formed and thermalized shock case (right panel). The targets are in the yez plane at x ¼ 0 and x ¼ 1 cm.
experiment using 1016 W/cm2 laser intensities from 10 drive beams at 500 J/beam in a 1 ns square pulse shape with the w300 mm diameter laser beam smoothing phase plates. At 5 ns, the most plausible interaction time, the velocity is vflow w 1000 km/s and ne w6 1018 cm2. When the laser turns on, plasma starts to flow at w103 km/s, so it takes (4 mm)/(103 km/s) ¼ 4 ns for the bulk of the flow to reach the region to be probed, which is the region simulated in Fig. 8(a). This is consistent with the peak in ne and ni at w4 ns in Fig. 8(a). As the laser is on for 1 ns, ne and ni do not continue to increase, but rather start to decrease after w4 ns. Using the output from LASNEX, we show in Fig. 8(b), the collision mean free path (solid) and characteristic length, [*ES , that is required to trigger the electrostatic plasma instability (red), calculated using Eq. (5). For electromagnetic instability length, [*EM , this is the length scaled by plasma skin depth, c/upi. In Fig. 8(b), the solid-blue line represents 300 c/upi. The factor of 300 is the estimate where the Weibel instability may start the shock formation based on the PIC simulations. The double foil experiments are difficult to simulate in LASNEX since it is a Lagrangian code with no collisionless effect. Thus we use experimentally measured plasma values to calculate the Coulomb mean free path, lmfp w 29.2 mm; c/upi w 0.12 mm; the characteristic electrostatic instability length from Eq. (5) is [*EM w2.34 mm, and the characteristic electromagnetic instability length from Eq. (6) is [*EM w1.2 mm assuming K ¼ 10. Our interaction length is w1 mm, thus we achieved c/upi < [*ES < [*EM w [int < lmfp. This is necessary but not sufficient for creating a collisionless shock. Increasing this separation of scales and increasing the duration of these conditions will be necessary to generate a collisionles shock. We next examine why we observe the high ion temperature for the double foil flow experiments. In order to understand the collisionless shock generation case, we simulate two flows with the measured plasma condition using the PIC code [22]. The PIC simulations indicate that the predicted ion temperatures prior to and after the formation of the (collisionless) shock are very different. The PIC simulation shows that the ion temperature can be as high as w3 keV when the shock is fully formed, shown in Fig. 9(d) on the right panel. So, our observation of w1 keV may be an indication that the shock is just starting to form. On the other hand, the center-of-mass energy of the colliding ions is w10 keV, so that a modest amount of collisional scattering might produce the ion “temperature” inferred from the data. Distinguishing between collisional and collisionless sources of transverse ion motion will be a significant challenge in the future.
Further, we examine the magnitude of the ion density and magnetic field filaments caused by the Weibel instability from the 2D PIC simulation using uniform plasmas whose parameters match the plasma conditions measured locally in our experiment. The left panel of Fig. 10 shows the ion density and the magnetic field formed by the counterstreaming plasmas at w4 ns. In this simulation, each flow was simulated with 1 1018 cm3 ion density as measured from the experiment. A fully formed shock should require the region with the ion density enhancement much greater than 2.0 1018 cm3, i.e., at least twice the density of the single flow. From this simulation, we can see that the shock is just beginning to form for parameters based on our experimental conditions. The self-generated magnetic field is small. The fully formed shock case is shown on the right panel. The clean shock formation required 5 1019 cm3 ion density from each stream. 4. Conclusion Our experiment demonstrated quantitative measurement of high velocity plasma flows. Based on the data and simulations, we conclude that weak Weibel mediated current filamentation and magnetic field generation were likely starting to occur in these experiments, but had not yet grown strong enough to be observed or to trigger shock formation. In the future we will continue experiments at Omega to optimize creation of the collisionless shocks and to identify signatures by probing the plasmas from different flow directions while attempting to create higher flow velocities and higher ne and ni. We will also measure the generated magnetic fields and distinguish their generation mechanisms, such as the “fountain field” (Vne VTe) mechanism in the non-interacting flow and the plasma instability generated fields in the interpenetrating interacting flows [23]. This experiment will be also performed at National Ignition Facility [24]. Our observations and experimental results will be important for understanding plasma processes occurring in astrophysical collisionless shocks, such as the generation of magnetic fields, and the acceleration of cosmic ray particles, which remain open questions of great interest in modern astronomy and astrophysics. Acknowledgments This work was performed under the auspices of the Lawrence Livermore National Security, LLC, (LLNS) under Contract No. DE-
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AC52-07NA27344. The work at Oxford University was funded by the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreements no. 256973 and 247039. M. Koenig was supported by the Institut Laser Plasma and A. Pelka was supported by the RTRA Triangle de la physique. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
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Studying astrophysical collisionless shocks with counterstreaming plasmas from high power lasers Hye-Sook Park a, *, D.D. Ryutov a, J.S. Ross a, N.L. Kugland a, S.H. Glenzer a, C. Plechaty a, S.M. Pollaine a, B.A. Remington a, A. Spitkovsky b, L. Gargate b, G. Gregori c, A. Bell c, C. Murphy c, Y. Sakawa d, Y. Kuramitsu d, T. Morita d, H. Takabe d, D.H. Froula e, G. Fiksel e, F. Miniati f, M. Koenig g, A. Ravasio g, A. Pelka g, E. Liang h, N. Woolsey i, C.C. Kuranz j, R.P. Drake j, M.J. Grosskopf j a
Lawrence Livermore National Lab, 7000 East Ave., Livermore, CA 94550, USA Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA c University of Oxford, Oxford, UK d Osaka University, Osaka, Japan e Laboratory for Laser Energetics, Rochester, NY, USA f ETH Science and Technology University, Zurich, Switzerland g Ecole Polytechnique, Paris, France h Rice University, Houston, TX, USA i University of York, Heslington, York, UK j University of Michigan, Ann Arbor, MI, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 November 2011 Accepted 1 November 2011 Available online 9 November 2011
Collisions of high Mach number flows occur frequently in astrophysics, and the resulting shock waves are responsible for the properties of many astrophysical phenomena, such as supernova remnants, Gamma Ray Bursts and jets from Active Galactic Nuclei. Because of the low density of astrophysical plasmas, the mean free path due to Coulomb collisions is typically very large. Therefore, most shock waves in astrophysics are “collisionless”, since they form due to plasma instabilities and self-generated magnetic fields. Laboratory experiments at the laser facilities can achieve the conditions necessary for the formation of collisionless shocks, and will provide a unique avenue for studying the nonlinear physics of collisionless shock waves. We are performing a series of experiments at the Omega and Omega-EP lasers, in Rochester, NY, with the goal of generating collisionless shock conditions by the collision of two highspeed plasma flows resulting from laser ablation of solid targets using w1016 W/cm2 laser irradiation. The experiments will aim to answer several questions of relevance to collisionless shock physics: the importance of the electromagnetic filamentation (Weibel) instabilities in shock formation, the selfgeneration of magnetic fields in shocks, the influence of external magnetic fields on shock formation, and the signatures of particle acceleration in shocks. Our first experiments using Thomson scattering diagnostics studied the plasma state from a single foil and from double foils whose flows collide “headon”. Our data showed that the flow velocity and electron density were 108 cm/s and 1019 cm3, respectively, where the Coulomb mean free path is much larger than the size of the interaction region. Simulations of our experimental conditions show that weak Weibel mediated current filamentation and magnetic field generation were likely starting to occur. This paper presents the results from these first Omega experiments. Published by Elsevier Ltd.
Keywords: Astrophysical Collisionless shocks Weibel instability Electromagnetic instabilities Interpenetrating plasmas Thomson scattering
1. Introduction Shock waves traveling >3000 km/s are observed in supernova remnants, such as in SN1006 [1]. Space and ground-based telescopes * Corresponding author. Tel.: þ1 925 422 7062; fax: þ1 925 423 6319. E-mail address: [email protected] (H.-S. Park). 1574-1818/$ e see front matter Published by Elsevier Ltd. doi:10.1016/j.hedp.2011.11.001
study astrophysical collisionless shocks observationally at many different wavelengths. As an example, Fig. 1 shows Chandra x-ray satellite observations of SN1006 in two different x-ray bands [2]. From these observations we can compare the shock thickness with the average Coulomb mean free path. The typical temperature and density behind the shock front is Ti w 15 keV (Te w 0.5e1 keV) and ni w 1 cm3. The corresponding proton Coulomb mean free path
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Fig. 1. (a) Profiles of the filaments in the SN 1006 northeast shell. Upper panels show the profiles in the (2.0e10.0 keV) band, whereas the lower panels in the (0.4e0.8 keV) band with the best-fit models (solid lines). The dashed lines in the lower panels represent nonthermal photons extrapolated from the hard band flux of the power law (upper panels). The dotted lines are the thermal component after subtracting the nonthermal contamination (dashed lines). Upstream is to the left and downstream is to the right. (b) Two-color images of SN 1006 northeast shell binned with 100 scale. Red and blue are 0.5e2.0 keV and 2.0e10.0 keV, respectively, both in logarithmic scale. [Reproduced from Bamba, ApJ, 2003]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
length is estimated to be 13 pc (¼4 1019 cm). The diameter of the entire SN1006 remnant is about 10 pc (¼3 1019 cm). The shock front width is about 0.04 pc (¼1.2 1017 cm). With these numbers, one concludes that the thickness of the shock front for SN1006 SNR is less than 1% of the radius and the Coulomb mean free path is 400 times longer than the shock front thickness, namely, the shock is collisionless [3]. Astrophysical shocks span a wide range of shock speeds, Mach numbers, magnetizations, and can occur in plasmas of varying composition, such as electron-ion or electron-positron plasmas. Despite their diversity, collisionless shocks share common characteristics: they are inferred to efficiently accelerate nonthermal particles and to generate and amplify magnetic fields, in addition to being able to effectively decelerate supersonic flows. As a result of the nonlinear plasma processes involved in the shock formation, the physics of such shocks remains unclear, and the conditions for efficient particle acceleration are not fully understood. It has been recently proposed [4,5,6,7] that the generation of magnetic fields can occur in these cosmic shocks on a cosmologically fast timescale via the Weibel (or filamentation) instability [8]. 3D particle-in-cell (PIC) numerical simulations have confirmed that the strength and scale of Weibel-generated magnetic fields are consistent with what would be required to play a dominant role in the magnetization of astrophysical collisionless shocks [9,10,11]. PIC simulations show how Weibel instabilities produce a magnetic field that mediates the formation of a shock at the interaction of unmagnetized plasma flows [12]. In Fig. 2(a), density filaments characteristic of the Weibel instability and the shock thus formed are visible, while Fig. 2(b) shows the density and the magnetic energy density in the shock region. The role of collisionless shocks is particularly important to the origin of ultrahigh energy cosmic rays (UHECR). While there is evidence that cosmic rays are primarily produced via first order Fermi acceleration at astrophysical shocks [13,14,15], the acceleration up to the knee, i.e., up to energies of 1015 eV, has challenged theorists for a long time. Recently, Bell [16] has proposed a novel mechanism for the amplification of magnetic fields by nonresonant interaction of cosmic ray driven currents with a preexisting magnetic field at the shock front. In this scenario, as the magnetic field changes the dynamics of shock acceleration, the maximum energy of the accelerated particles is amplified by orders of magnitude.
In astrophysical plasmas, there is no way to directly measure the key quantities to investigate the shock dynamics and particle acceleration by collisionless shocks. Our proposed investigations will address the underlying physics of collisionless shock formation via scaled laser experiments. Analytic estimates indicate that scaling from astrophysical scales to laboratory experiments at the Omega and Omega-EP lasers should be possible. 1.1. Laboratory collisionless shock experimental consideration The geometry of the experimental configuration is shown in Fig. 3. Two high velocity plasma flows are generated by ablation from two planar targets oriented to intersect at some point in between. We want to satisfy two conditions: 1. The collision mean free path lmfp for the more massive ion component (carbon, in the case of CH plasmas) should be much larger than the system size (that is, the spatial scale of the interacting flows, [int ): lmfp >> [int . 2. The system size, [int , must be much larger than the scale, [* , needed to generate plasma instabilities: [int >> [* . So, we are looking for the conditions where
[* [int lmfp
(1)
Fig. 3 illustrates the geometry: this figure corresponds to a limiting case where the flows interpenetrate with each other. If, however, the interaction (collisionless or collisional) is strong, then strong shocks are formed in the intersection region, flow velocity decreases, and the plasma is heated. For example, for CH flows with a velocity of 108 cm/s intersecting at an angle of a ¼ 45 , heating to a temperature of Ti w 3e5 keV is predicted to occur in a collisionless shock (see discussion of Fig. 9). This could be detected by a variety of techniques. In particular, one flow made of CH interacting with another flow of CD will produce neutrons according to the strength of their interaction. Since the temperature of a noninteracting flow is relatively low, DD (nuclear) reactions in the isolated CD flow will be weak. They will be weak also in the case where two flows pass through each other without interaction. Conversely, if the interaction is strong, e.g., a collisionless shock is formed, deuterium will be heated to a high temperature, and
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Fig. 2. (a) Filamentary density structure in an unmagnetized shock mediated by the Weibel instability as simulated by a 3D PIC code [Reproduced from Spitkovsky, AIP 2005]. Color represents density: yellow corresponds to high, green to intermediate, and black to low density. The green striations are density filaments caused by the Weibel instability, and are a precursor to collisionless shock formation. The increase in density (transition from green to yellow) indicates the formation of a shock. The incoming flow propagates from the lower left to the upper right, and the shock moves to the lower left; (b) Density structure through the unmagnetized shock (solid line, left axis) and magnetic energy normalized by the upstream kinetic energy (thin line, right axis). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
a measureable burst of DD-produced neutrons should occur at the intersection time. When evaluating lmfp, we assume that the temperature of the colliding flows is much smaller than the ion energy due to the bulk flow velocity; this is consistent with LASNEX radiationhydrodynamics simulations. In this case, the numerical estimate for lmfp can be presented as:
lmfp ðcmÞw5
A2 1013 4Z Z
a ½vðcm=sÞ cos4 2 nz cm3 4
(2)
where AZ, Z, and nZ are the atomic weight, charge, and number density of the main ion component, and v is the flow bulk velocity before the collision with the other flow. This equation is based on Eq. (14.12) of Ref. [17], with the Coulomb logarithm assumed to be 10. The cos(a/2) factor is related to the center-of-mass effect. A numerical example is helpful: for v ¼ 108 cm/s, Az ¼ 12, Z ¼ 6, nZ¼1018 cm3, and a ¼ p/2, one finds lmfpw1.5 cm. Evaluating [* is a formidable task; present-day computer codes and computing power are still not up to this task. This makes the proposed experiment all the more interesting and adds importance to the whole endeavor. A possible heuristic model (based on the growthrate assessments similar to those presented in Ref. [18]) for evaluating [*ES for electrostatic plasma instabilities can be presented as
[*ES wK
v W upi Te
(3)
where K >> 1 is a numerical factor accounting for the number of the growth times required for the instability to reach a developed stage, W is the kinetic energy of the main ion component in the flow, Te is the electron temperature (in energy units) in the flow prior to the collision, v is the bulk flow velocity, and upi is the ion plasma frequency. Note, v/upi is roughly the distance traveled by the flow in one ion plasma wave oscillation period. Hence, K >> 1 implies that the plasma in the interaction region should correspond
Fig. 3. The geometry of the proposed experiment. The condition for collisionless shock creation is: [* [int lmfp where [* is the plasma interaction length threshold for triggering plasma instabilities.
to many (>>1) plasma waves. Numerically inserting characteristic values gives:
WðeVÞ ¼ 5:2 1013 Az ½vðcm=sÞ2 For
[*ES,
(4)
the numerical estimate is:
pffiffiffiffiffiffi
vðcm=sÞ AZ [*ES ðcmÞw103 K qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z nz cm3
WðeVÞ Te ðeVÞ
(5)
For K ¼ 30, v ¼ 108 cm/s, Az ¼ 12, Z ¼ 6, nZ¼1018 cm3, and Te ¼ 600 eV, the length [*ES is 0.18 cm. If one takes the estimate in Eq. (5) compared to Eq. (2) at face value, the optimum conditions for the study of collisionless shocks favor higher flow energies and electron temperatures, and lower flow densities, limited of course by diagnostic sensitivities and constraints. Lower-Z materials are somewhat preferable as lmfp very rapidly increases for lower-Z. Estimates from Eqs. (3) and (5) correspond to that for an electrostatic instability, which will probably be dominant at the initial stage of interaction. For the electromagnetic instability, [*EM , of the Weibel type, the estimate corresponding to Eq. (3) would be
[*EM wK
c
upi
; where K>1
(6)
Here, c/upi corresponds to ion plasma skin depth, namely, the distance light could travel in one ion plasma wave oscillation period. For the characteristic parameters mentioned above, estimates from Eqs. (3) and (6) yield the same or of magnitude results. Of course, one has to interpret these estimates with care, as there is no widely accepted nonlinear theory for the problem with which we are concerned. In this regard, our experiment will guide the theory and simulations. One of the concerns for the proposed experiment is the possible presence of a regular magnetic field, generated in the course of the flow formation at the targets. This field could then be advected with the flow. The collision of two flows with embedded magnetic fields could produce a big splash (literally and figuratively), even if there are no micro-instabilities present. This may be an effect that is very interesting in its own right. If a magnetic field is generated by the Vne VTe, “fountain field” mechanism, it will be predominantly azimuthal. The axial current driven by the laser-ablated plasma would flow outwards normal to the target near the axis and in the opposite direction at larger radii, somewhat like a current “fountain”, closing radially near the flow end. This field will have a relatively minor effect on the interpenetration of the ions if the ion gyro-radius in the field is significantly larger than [*EM . The gyro-radius can be evaluated as:
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Fig. 4. The Dec 2010 Omega experimental geometry for the (a) single and (b) double foil cases. The laser intensity on the target was 8 1015 W/cm2.
pffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi AZ WðeVÞ Z BðkGÞ
ri ðcmÞw0:15
(7)
Introducing the plasma b, the ratio of the plasma particle pressure to the magnetic pressure, one can write: 9
BðkGÞw6 10
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ne cm3 Te ðeVÞ
b
(8)
For ne ¼ 1019, and Te ¼ 103 eV, one has B(kG) w 600/Ob. For b w 100, B w 60 kG, and the ion gyro-radius (for carbon ions with
the energy of 60 keV), according to Eq. (6), is w0.4 cm. This shows that the flows have to be characterized individually with respect to the regular magnetic field. The effect of the regular field will be present for the head-on collisions of flows (a ¼ 0). The magnetic field that would affect the interpenetration of the electrons of the two flows will be much weaker than that required to affect the ions, as the electron gyro-radius is much smaller than the ion gyroradius. However, the inhibition of mixing of electrons of the two flows may not have too strong an effect on the interpenetration of the ions, provided the directed ion energy is much higher than their pre-collision thermal energy.
The basic requirements for creating a collisionless shock in the laboratory are that ([*ES , [*EM ) << [int << lmfp: namely, the shock thickness [* determined by electrostatic or electromagnetic (Weibel) instabilities needs to be smaller than spatial scale of the interacting plasmas (the experimental scale), and these lengths should be much less than the Coulomb mean free path length. We report our first experiment to study the plasma condition generated by counterstreaming plasmas. The plasma temperature, density and the flow velocities were measured by Thomson Scattering using a 0.53 mm probe laser on Omega. 2. Experimental results Our first Omega experiment concentrated on measuring and understanding the plasma conditions that are created by the Omega lasers on single and double foil configurations. Thomson scattering was used to characterize the plasma created by 10 heater-drive beams incident on a CH foil. All our 12 shots produced high quality data with 2 different laser intensities, 3 different probe times, in single and double foil geometry. The heater-drive beams deliver 5 kJ of energy in a 1 ns square pulse shape. The target geometry is shown in Fig. 4. A probe beam of 0.53 mm wavelength
Fig. 5. An example of Thomson scattering data and the fit for a single foil shot. (a) ion features; (b) electron features; (c) ion features data and fit; (c) electron features data and fit. A time slice of the ion and electron features are simultaneously fit to produce Te, Ti, ne, vflow, udrift parameters.
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Fig. 6. Data from double foil shows much higher ion temperature and higher electron density indicating stagnation of the plasmas. The flow velocity is also reduced systematically for the double foil flows.
Fig. 7. Measured plasma parameters from a single foil flow compared with a 2-D hydrodynamics simulation. The measured electron temperature is high compared to that simulated, which may be due to the probe beam heating. Blue points are single foil data with laser intensities of 8 1015 W/cm2; green are single foil data with laser intensities of 8 1014 W/cm2; red are double foil data with 8 1015 W/cm2 on each foil; the black line is the 2-D LASNEX simulation for the single foil with 8 1015 W/cm2. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 8. 2-D radiation-hydrodynamics simulations from LASNEX at 4 mm distance from the target: (a) velocity, ne, ni, Te, Ti, vflow as function of time; (b) Collision mean free path (black) and characteristic electrostatic instability (red) and ion skin depth, c/upi (blue-dotted). The electromagnetic instability length is 10e300 of ion skin depth (drawn in this figure is 300 c/upi.) for collisionless shocks, [*ES or EM < lmpf condition is required. (c) 2-D LASNEX simulations show the distribution of electron density (left) and azimuthal magnetic field (right) in r-z space at 2 different times. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
(labeled “2u probe” in the figures) is pointed 4 mm from the foil surface. The Thomson-scattered (TS) light of the 2u probe laser in the plasma is collected with an f/10 optic on a Ten Inch Manipulator in TIM-6 at a distance of 50 cm from the plasma. Detailed description of this instrument can be found in Ref. [19]. The Thomson scattering probe volume was 100 mm 100 mm 60 mm defined by the optical magnification and the overlap of the streak camera slit (100 mm) and the spectrometer slit (100 mm), in the plasma with the probe beam, which was focused to 60 mm diameter. We chose the target axis such that the k-vector is normal to the target normal measuring the plasma condition along the plasma flow direction. In our current set-up, the Thomson scattering observes the projection of the velocity along the ion-acoustic wave k-vector. Thomson scattering was measured from the electron feature (collective scattering from electron-plasma waves) and the ion feature (collective scattering from ion-acoustic waves). An example of electron and ion features from a single foil shot is shown in the top panel of Fig. 5. Our data set includes temporal measurements from 2.0 to 3.0 ns, 5.0e6.0 ns, and 7.8e8.8 ns. Time-slices of the data from the electron feature are then fit with the Thomson scattering form factor that allows a measurement of the electron temperature (Te) and electron density (ne) [20]. With constraints from the electron feature fit, the ion feature can then be used to measure the ion temperature (Ti) and bulk plasma flow velocity (vflow). This can be understood from the simplified dispersion rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4lprobe ZTe 3Ti sinðq=2Þ þ . An example of fitting relation, Dl ¼ c M M the results is shown in the bottom panel of Fig. 5. The double foil data also showed very interesting results. The difference between the single foil and the double foil data for the ion feature is striking, as shown in the left panel of Fig. 6. A similar
fitting procedure was applied to the double foil data set. Fig. 6 shows the results at 8.6 ns after the laser pulse. Compared to the single foil flow, the ion temperature and electron density are considerably higher. Another observation is that the flow velocity is reduced for all the double foil flows indicating interaction between the two flows at late in time. The measured plasma characteristics from different shots covering a 2e9 ns time interval and single and double foils are compiled in Fig. 7, where the flow velocity, electron density, ion temperature and electron temperature are shown. Different color data points represent different experimental conditions of single foil shots (blue), double foil shots (red), and single foil with 10 times lower drive laser intensity (green). The data is compared to 2D LASNEX [21] hydrodynamic simulations, indicated by the solid black curves. There is good agreement between the measured and simulated bulk plasma flow velocity over all three time intervals. The measured electron density shows a sharp increase between 5.0 and 6.0 ns, which is also present in the simulations, indicating that the bulk of plasma arrives at this time. This is consistent with flow arrival at the 4 mm location of the plasma flow with velocity of w103 km/s. The measured electron temperature is significantly higher than the simulations. We attribute this to reheating the plasma by the TS probe beam. The measured ion temperature is consistent with the 2D simulations. An electron temperature of 170 eV had to be assumed during this time interval due to a lack of electron feature data. 3. Discussion In order to see whether our experimental results meet the requirements for creating a collisionless shock, we examine the 2-D LASNEX simulation of a single foil for the plasma conditions of our
Fig. 9. PIC simulations of electron and ion distribution functions when the shock is just beginning to form (left panel) compared to when the shock is fully formed (right panel). Note the asymmetry of the ion velocity distribution (b) versus symmetry (d) depending on the shock-forming stage. This signature can be utilized to identify the time when the shock is fully forming.
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Fig. 10. PIC simulation of shock creation using the measured plasma condition from our experiment (left panel) and fully formed and thermalized shock case (right panel). The targets are in the yez plane at x ¼ 0 and x ¼ 1 cm.
experiment using 1016 W/cm2 laser intensities from 10 drive beams at 500 J/beam in a 1 ns square pulse shape with the w300 mm diameter laser beam smoothing phase plates. At 5 ns, the most plausible interaction time, the velocity is vflow w 1000 km/s and ne w6 1018 cm2. When the laser turns on, plasma starts to flow at w103 km/s, so it takes (4 mm)/(103 km/s) ¼ 4 ns for the bulk of the flow to reach the region to be probed, which is the region simulated in Fig. 8(a). This is consistent with the peak in ne and ni at w4 ns in Fig. 8(a). As the laser is on for 1 ns, ne and ni do not continue to increase, but rather start to decrease after w4 ns. Using the output from LASNEX, we show in Fig. 8(b), the collision mean free path (solid) and characteristic length, [*ES , that is required to trigger the electrostatic plasma instability (red), calculated using Eq. (5). For electromagnetic instability length, [*EM , this is the length scaled by plasma skin depth, c/upi. In Fig. 8(b), the solid-blue line represents 300 c/upi. The factor of 300 is the estimate where the Weibel instability may start the shock formation based on the PIC simulations. The double foil experiments are difficult to simulate in LASNEX since it is a Lagrangian code with no collisionless effect. Thus we use experimentally measured plasma values to calculate the Coulomb mean free path, lmfp w 29.2 mm; c/upi w 0.12 mm; the characteristic electrostatic instability length from Eq. (5) is [*EM w2.34 mm, and the characteristic electromagnetic instability length from Eq. (6) is [*EM w1.2 mm assuming K ¼ 10. Our interaction length is w1 mm, thus we achieved c/upi < [*ES < [*EM w [int < lmfp. This is necessary but not sufficient for creating a collisionless shock. Increasing this separation of scales and increasing the duration of these conditions will be necessary to generate a collisionles shock. We next examine why we observe the high ion temperature for the double foil flow experiments. In order to understand the collisionless shock generation case, we simulate two flows with the measured plasma condition using the PIC code [22]. The PIC simulations indicate that the predicted ion temperatures prior to and after the formation of the (collisionless) shock are very different. The PIC simulation shows that the ion temperature can be as high as w3 keV when the shock is fully formed, shown in Fig. 9(d) on the right panel. So, our observation of w1 keV may be an indication that the shock is just starting to form. On the other hand, the center-of-mass energy of the colliding ions is w10 keV, so that a modest amount of collisional scattering might produce the ion “temperature” inferred from the data. Distinguishing between collisional and collisionless sources of transverse ion motion will be a significant challenge in the future.
Further, we examine the magnitude of the ion density and magnetic field filaments caused by the Weibel instability from the 2D PIC simulation using uniform plasmas whose parameters match the plasma conditions measured locally in our experiment. The left panel of Fig. 10 shows the ion density and the magnetic field formed by the counterstreaming plasmas at w4 ns. In this simulation, each flow was simulated with 1 1018 cm3 ion density as measured from the experiment. A fully formed shock should require the region with the ion density enhancement much greater than 2.0 1018 cm3, i.e., at least twice the density of the single flow. From this simulation, we can see that the shock is just beginning to form for parameters based on our experimental conditions. The self-generated magnetic field is small. The fully formed shock case is shown on the right panel. The clean shock formation required 5 1019 cm3 ion density from each stream. 4. Conclusion Our experiment demonstrated quantitative measurement of high velocity plasma flows. Based on the data and simulations, we conclude that weak Weibel mediated current filamentation and magnetic field generation were likely starting to occur in these experiments, but had not yet grown strong enough to be observed or to trigger shock formation. In the future we will continue experiments at Omega to optimize creation of the collisionless shocks and to identify signatures by probing the plasmas from different flow directions while attempting to create higher flow velocities and higher ne and ni. We will also measure the generated magnetic fields and distinguish their generation mechanisms, such as the “fountain field” (Vne VTe) mechanism in the non-interacting flow and the plasma instability generated fields in the interpenetrating interacting flows [23]. This experiment will be also performed at National Ignition Facility [24]. Our observations and experimental results will be important for understanding plasma processes occurring in astrophysical collisionless shocks, such as the generation of magnetic fields, and the acceleration of cosmic ray particles, which remain open questions of great interest in modern astronomy and astrophysics. Acknowledgments This work was performed under the auspices of the Lawrence Livermore National Security, LLC, (LLNS) under Contract No. DE-
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AC52-07NA27344. The work at Oxford University was funded by the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreements no. 256973 and 247039. M. Koenig was supported by the Institut Laser Plasma and A. Pelka was supported by the RTRA Triangle de la physique. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
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