Magnetic Disruption of Inertially Collimated Flows on the Titan Laser Facility

Transcription

1 Magnetic Disruption of Inertially Collimated Flows on the Titan Laser Facility B = 1 mm n e [1 18 cm -3 ] 1 Mario Manuel Magnetic Meeting University of Rochester Laboratory for Laser Energetics April 23 rd, 218 Manuel et al. HEDP 17 (215) Manuel et al. PRL (submitted)

2 Magnetic Disruption of Inertially Collimated Flows on the Titan Laser Facility B = 1 mm B n e [1 18 cm -3 ] 1 Mario Manuel Magnetic Meeting University of Rochester Laboratory for Laser Energetics April 23 rd, 218 Manuel et al. HEDP 17 (215) Manuel et al. PRL (submitted)

3 Magnetic Disruption of Inertially Collimated Flows on the Titan Laser Facility B = B = 2 T B = 5 T 1 mm n e [1 18 cm -3 ] 1 Mario Manuel Magnetic Meeting University of Rochester Laboratory for Laser Energetics April 23 rd, 218 B 1 1 Manuel et al. HEDP 17 (215) Manuel et al. PRL (submitted)

4 Magnetized plasma jets are readily created in the lab for the study of plasmas relevant to astrophysical systems Inertially collimated, supersonic plasmas may be magnetically disrupted by an axial B-field At high enough Re m, inertia-dominant systems (ρv 2 >> B 2 /2μ ) may disrupt due to amplification of even a weak axial B-field

5 Collaborators M. J.-E. Manuel, A. M. Rasmus, C. C. Kuranz, S. R. Klein, M. J. MacDonald, J. Davis, M. R. Trantham, J. R. Fein, P. X. Belancourt, R. P. Young, P. A. Keiter, R. P. Drake University of Michigan B. B. Pollock, J. Park, A. U. Hazi, G. J. Williams, H. Chen Lawrence Livermore National Laboratory Support for this work was provided by NASA through Einstein Postdoctoral Fellowship grant number PF awarded by the Chandra X-ray Center, which is operated by the Astrophysical Observatory for NASA under contract NAS8-36, by the NNSA- DS and SC-OFES Joint Program in High-Energy-Density Laboratory Plasmas, grant number DE-NA184 and by the Predictive Sciences Academic Alliances Program in NNSA-ASC via grant DEFC52-8NA Work by LLNL was performed under the auspices of U.S. DOE under contract DE-AC52-7NA27344.

6 The dynamics and evolution of collimated plasma flows are important to astrophysical accretion systems HH 8/81 YSOs, AGN, PNe, and ppne Magnetic collimation (magnetic tower) Inertial collimation (shock-focused inertial confinement)

7 Jets are produced from laser-irradiated plastic targets θ c ~8 expanding plasma λ =.527 μm τ~1 ns ~6 μm spot 9-μm-thick plastic cone plasma jet collimates onaxis

8 Axial B-field [T] Plasma jets are magnetized externally using a custom-built, pulse-power solenoid B T».43I ka fit to data analytic solution Solenoid Current [ka] probe Side View 12.7 mm B-field The axial B-field at the gap center is linearly proportional to the current and within 2% of the analytic solution.

9 Optical interferometry characterizes the spatial profile of inertially-confined plasma flows Interferometry Probe Beam λ=.532 μm

10 Optical interferometry characterizes the spatial profile of inertially-confined plasma flows raw interferogram collimated 1 mm jet Interferometry Probe Beam λ=.532 μm Dj free» ò æ ç è - n e 2n cr ö w ø c dl

11 Processed interferograms show collimated flows when no axial B-field is applied B = 1 mm n e [1 18 cm -3 ] 1

12 A 5-T B-field applied along the jet axis disrupts axial collimation B = B = 5 T 1 mm B n e [1 18 cm -3 ] 1 1

13 Jet-disruption effectiveness depends on the B-field strength B = B = 2 T B = 5 T 1 mm n e [1 18 cm -3 ] A 5-T axial B-field disrupts the inertially-collimated region of the flow, and magnetically collimates the radially expanding plasmas

14 A Lagrangian model* analytically accounts for B-field advection and diffusion in a converging cylindrical plasma R initial condition time t later R = R τ Dimensionless metric for time V B V τ L L B L L = L +V t *Fedorov CESW 41 (25) Uniform, incompressible, constant V Axial B-field B penetrating the volume Elongation occurs in time due to collimation (dr/dt<)

15 A Lagrangian model* analytically accounts for B-field advection and diffusion in a converging cylindrical plasma B(r,t) = B te - t 2-1 2Re m æ Re m = R ö ç V R è 4L øh / m Ratio of B-field advection to diffusion *Fedorov CESW 41 (25)

16 A Lagrangian model* analytically accounts for B-field advection and diffusion in a converging cylindrical plasma B(r,t) = B te - t 2-1 2Re m æ Re m = R ö ç V R è 4L øh / m Linear amplification Ratio of B-field advection to diffusion *Fedorov CESW 41 (25)

17 A Lagrangian model* analytically accounts for B-field advection and diffusion in a converging cylindrical plasma B(r,t) = B te - t 2-1 2Re m æ Re m = R ö ç V R è 4L øh / m Linear amplification Ratio of B-field advection to diffusion Diffusion becomes more important with increasing τ (shrinking radius) *Fedorov CESW 41 (25)

18 A Lagrangian model* analytically accounts for B-field advection and diffusion in a converging cylindrical plasma B(r,t) = B te - t 2-1 2Re m æ Re m = R ö ç V R è 4L øh / m 6 Re m = 1-1 Re m = 1 2 B max B».6 Re m 4 B,t ( ) B 2 Re m = 1 1 t max = Re m Re m = t

19 A collimation parameter (ψ) is derived from the on-axis pressure normalized to the magnetic pressure b dyn = rv 2 æ 2 B Re m = R ö ç V R y = 1 2 æ R ö b dyn ç - b th 4L 2m è øh / m 4 t 3 t -t 2 e - t 2-1 Re m è L ø Inertial Collimation

20 A collimation parameter (ψ) is derived from the on-axis pressure normalized to the magnetic pressure b dyn = rv 2 æ 2 B Re m = R ö ç V R y = 1 2 æ R ö b dyn ç - b th 4L 2m è øh / m 4 t 3 t -t 2 e - t 2-1 Re m è L ø Inertial Collimation Thermal Expansion

21 A collimation parameter (ψ) is derived from the on-axis pressure normalized to the magnetic pressure b dyn = rv 2 æ 2 B Re m = R ö ç V R y = 1 2 æ R ö b dyn ç - b th 4L 2m è øh / m 4 t 3 t -t 2 e - t 2-1 Re m è L ø Inertial Collimation Thermal Expansion Magnetic Expansion

22 A collimation parameter (ψ) is derived from the on-axis pressure normalized to the magnetic pressure b dyn = rv 2 æ 2 B Re m = R ö ç V R y = 1 2 æ R ö b dyn ç - b th 4L 2m è øh / m 4 t 3 t -t 2 e - t 2-1 Re m è L ø Inertial Collimation Thermal Expansion Magnetic Expansion y < : Jet Disruption y > : Jet Formation

23 The Lagrangian-cylinder model describes observations well in a semi-quantitative manner at 5 ns (τ~25) β dyn β dyn β dyn = B = 2 T B = 5 T B = 1 mm n e [1 18 cm -3 ] 1 1 1

24 The Lagrangian-cylinder model describes observations well in a semi-quantitative manner at 5 ns (τ~25) ψ β dyn β dyn β dyn = B = 2 T B = 5 T B = 1 mm n e [1 18 cm -3 ] Jet Formation Re m = 2-1 B = 5 T Jet Disruption Elongation Factor (τ)

25 The Lagrangian-cylinder model describes observations well in a semi-quantitative manner at 5 ns (τ~25) ψ β dyn β dyn β dyn = B = 2 T B = 5 T B = 1 mm n e [1 18 cm -3 ] B = 2 T 1 Jet Formation Re m = 2-1 B = 5 T Jet Disruption Elongation Factor (τ)

26 Similar behavior is observed* in magnetized shaped charges B =.84 T B = 1.4 T *Fedorov JAMTP 48 (27)

27 B-field amplification can quickly cause jet disruption at high enough magnetic Reynolds numbers ψ β dyn = 1 3 Jet Formation Re m = Jet Disruption Elongation Factor (τ)

28 B-field amplification can quickly cause jet disruption at high enough magnetic Reynolds numbers ψ ψ β dyn = 1 3 Jet Formation Re m = 1-1 Re m = Jet Disruption Elongation Factor (τ) β dyn = 1 3 Higher Re m pushes ψ < at earlier τ Elongation Factor (τ)

29 B-field amplification can quickly cause jet disruption at high enough magnetic Reynolds numbers ψ The presence of even a weak axial B-field in a hydrodynamically converging system will disrupt collimation at high enough Re m In astrophysical accretion systems Re m > 1 1, observations of a weak B-field parallel to the outflow* precludes inertial-collimation as a source Re m = β dyn = 1 3 * Targon ApJ 743 (211) Elongation Factor (τ)

30 Magnetized plasma jets are readily created in the lab for the study of plasmas relevant to astrophysical systems Inertially collimated, supersonic plasmas may be magnetically disrupted by an axial B-field At high enough Re m, inertia-dominant systems (ρv 2 >> B 2 /2μ ) may disrupt due to amplification of even a weak axial B-field

31 Backup Slides

32 B-field diffusion may be estimated using the magnetic Reynolds number τ d L2 D m Re m = VL D m τ d L V Re m For experimental parameters, L~1 mm and V~5 km/s, τ d 2Re m [ns] Magnetic Reynolds numbers of ~2 suggest diffusion times of order 4 ns, significantly longer than the experimental time scale

33 Radial pressure balance determines if the plasma cylinder continues to collimate Radial Pressure Balance Central Axis Pressure (r/r) 2 << 1 r dv r dt = - p r + j fb z p c = 1 4 y < : Jet Disruption y > : Jet Formation æ ç è R L Collimation Parameter y = 1 æ ç 4 è R L ö ø ö ø 2 2 rv 2 t 3 b dyn t 3 - p th, t - B 2 t 2 e - 2m t 2-1 Re m Normalize to Magnetic Pressure - b th t -t 2 e - t 2-1 Re m Inertial Collimation Thermal Expansion Magnetic Expansion

34 Interferometry is used to measure the free-electron density and diagnose the evolution of the plasma jet raw interferogram collimated 1 mm jet mask smoothed data Dj free» ò æ ç è - n e 2n cr ö w ø c dl n e [1^18 cm -3 ] 1 Abel-transformed data of the top and bottom are averaged to create a symmetric image (Δ err < 3%)

35 Interferometry is used to measure the free-electron density and diagnose the evolution of the plasma jet raw interferogram collimated 1 mm jet Dj free» ò æ ç è - n e 2n cr ö w ø c dl mask smoothed data n e [1^18 cm -3 ] 1 1 Dj meas < Dj free n e > n cr p Abel-transformed data of the top and bottom are averaged to create a symmetric image (Δ err < 3%) Abel Transform ò r d(dj meas ) dy dy y 2 - r 2

36 Radiation-hydrodynamic calculations predict inertial collimation in the breakout plasma of conical targets 3 mm log 1 ρ [g/cc] log 1 1 p th [bar] 1 6 v z [km/s] -1 1 v r [km/s] -2 2 log 1 ρ [g/cc] log 1 p th [bar] B = 5 ns v z [km/s] v r [km/s] Schematic FLASH Results

37 Pinching in this geometry is proposed as a mechanism that can form astrophysical jets from isotropic, stellar outflows r [mm] log 1 n e [1 18 /cc] v z [km/s] z [mm]

38 Proton radiography suggests that jet collimation is not aided by self-generated B-fields Proton Fluence high 1 mm E~1.1 MeV T +45 ps E~7.6 MeV T +52 ps E~5. MeV T +65 ps E~2.3 MeV T +95 ps low Lack of proton deflections at the jet location indicate hydrodynamic collimation.

39 m 1 mm 1 mm Processed interferograms indicate collimated jet formation collimated jet +2π -2π Interferograms show fringe shifts Wavelet analysis reveals the phase change distribution n e [1 18 #/cc]

40 <Z> FLYCHK Results Atomic Composition of the Cone: C 5 H 8 O 2 Trace Sb.3 <A> = 6.7 <Z> = 3.6 (essentially acrylic) 1.E E-2 T e = 1.5 ev T e = 1. ev At low ionization states maybe coulomb interactions with neutrals becomes important. Quick calculations indicate that at Z~.1, Te=1eV and ne=1e18, that CM x-section is ~1 times less than plasma x-section E E T e =.5 ev 1.E-8 1.E E E E+2 1 n e [cm -3 ] At T ~1eV in the density regimes of interest <Z>~

41 Plasma flows in transverse B-fields are relevant to a variety of astrophysical plasmas B pol B`pol B θ Collimating Force F^ = - B q m r Ñ^ self-collimation ( rb q ) + j q B pol pinching Herbig-Haro Object HH3

42 Normalized Axial Field [T/kA] B-field measurements demonstrate a <5% spatial variation within a 2.5 mm radius of the gap center. A custom-designed ~1-mm 3 B-dot probe spatially resolved the axial magnetic-field strength in the solenoid gap bridge side open side analytic solution Radius [mm] bridge B-field open Top View 12.7 mm probe

43 9.9 mm A custom-designed solenoid provided a constant field while still allowing diagnostic access D ~ 5 mm 7 mm 5 T L ~ 4 mm The 5 T point design generates plasma betas down to β th ~.2 (n ~ 1 18 cm -3, T~1 ev)

44 Magnetohydrodynamic (MHD) equations describe both laboratory and astrophysical systems Continuity Momentum r + Ñ rv = t æ r ç v è t + v Ñv ö = -Ñp + 1 Ñ B ø m ( ) B Energy Field Evolution p t -g p r r t + v Ñp -g p r v Ñr = B t = Ñ v B ( ) Ryutov, ApJ 518 (1999); Ryutov, POP 8 (21); Drake, High-energy-density physics (26), ch 1; Remington, RMP 78 (26)

45 Magnetohydrodynamic (MHD) equations describe both laboratory and astrophysical systems Thermoelectric term typically dominates field generation Combine the Electron Momentum Equation and Faraday s Law: Conservation of Generalized Vorticity Electron B-field Convection Thermoelectric Field Generation j X B Force Term Most terms describe B-field evolution in time and space Pressure Tensor is typically small relative to other terms Pressure Tensor Term Thermal and Frictional Forces

46 Multiple dimensionless parameters determine the validity of using the MHD equations to describe system dynamics The system exhibits fluid-like behavior l mfp L <<1 Energy flow by particle heat conduction is negligible Pe >>1 Energy flow by radiation flux is negligible Pe g >>1 Viscous dissipation is negligible Re >>1 Astrophysical systems are large and fulfill these criteria in many cases!

47 Multiple dimensionless parameters determine the validity of using the MHD equations to describe system dynamics The system exhibits fluid-like behavior l mfp L <<1 Energy flow by particle heat conduction is negligible Pe >>1 Energy flow by radiation flux is negligible Pe g >>1 Viscous dissipation is negligible Re >>1 Two MHD systems evolve similarly when the Euler number (Eu) and beta (β) are similar. Eu º v * b º p * p * r * B * ( ) 2

48 Magnetized plasma jets are prominent in young stellar objects with a wide range of parameters Physical condition Constraint YSO Jets Experiment Viscosity plays minor role Reynolds ~ ~ Magnetic diffusion plays minor role Magnetic Reynolds ~ ~ Supersonic flow Mach number ~ ~1-1 1 Thermal compared to magnetic pressure Dynamic compared to magnetic pressure Thermal plasma β th ~ ~1-1 5 Dynamic plasma β dyn ~ ~ Curran et al., MNRAS 382 (27); Carrasco-Gonzalez et al., Science 33 (21); Ferreira AA 452 (26); Reipurth ARAA 39 (21)