Investigation of magnetized non-neutral complex plasmas

Transcription

1 Investigation of magnetized non-neutral complex plasmas M. Romé 1, F. Cavaliere 1, M. Cavenago 2, F. Lepreti 3, G. Maero 1, B. Paroli 1, R. Pozzoli 1 1 Dipartimento di Fisica, Università degli Studi di Milano, and INFN Sezione di Milano, Italy 2 INFN Laboratori Nazionali di Legnaro, Italy 3 Dipartimento di Fisica, Università della Calabria, and CNISM Unità di Cosenza, Rende, Italy Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 1

2 Introduction [1] Complex or dusty plasmas are ionized gases that also contain a distribution of micrometer-sized particles with a surface charge of the order of a few thousand electron charges. These plasmas are characterized by the interplay between a wide range of time and spatial scales, and the presence of new physical phenomena with respect to normal plasmas [Morfill & Ivlev, RMP 2009]. Laboratory complex plasmas generally satisfy a global (quasi-)neutrality condition. Recently the concept of magnetization of a dusty plasma has drawn a considerable interest [Thomas Jr. et al., PPCF 2012]. A magnetic field may influence the dust charging process and hence the electrostatic interaction between the dust grains, their diffusion, equilibrium distribution and confinement time, affecting in turn the dynamics of the overall plasma. Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 2

3 Introduction [2] Magnetized non-neutral plasmas (i.e., plasmas of particles with the same sign of charge) can be easily confined for long times in Penning-Malmberg traps [Malmberg & degrassie, PRL 1975] under ultra-high vacuum (UHV) conditions (residual gas pressure 10-8 mbar) with a combination of static electric and magnetic fields, and their evolution can be monitored by means of electrostatic and optical systems. PM-trap operation: inject / hold and manipulate /dump and measure Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 3

4 Penning-Malmberg Trap Unimi Parameter Typical range n e cm -3 B T e P V L p R 0.2 T 1-10 ev mbar 100 V cm 4.5 cm Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 4

5 DuEl (Dust-Electron) Project The DuEl (Dust-Electron) research project aims at studying experimentally and with the help of theoretical and numerical tools a magnetized nonneutral complex plasma. The project involves the construction of an apparatus (modified Penning- Malmberg trap) for the confinement of a plasma of electrons contaminated by a dust population and by a fraction of light positive ions (transient or confined by means of proper electrostatic potentials; variable degree of neutrality). A specific target is the the study of the dynamics of an electron plasma, its fluid instabilities, the evolution of the 2D turbulence and the formation of coherent structures in the presence of a charged dust population [partial support by MIUR PRIN 2009 funds; Romé et al., on Non-Neutral Plasma Physics VIII, AIP Proc (2013)]. Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 5

6 Parameters of a dusty plasma (a few ) dust radius = a dust mass density = ρ d dust charge = Q d, dust charge number = Z d = Q d /e electron, ion and neutral atom mass = m e, m i, and m n, respectively dust mass = m d = 4πa 3 ρ d /3 (spherical grains) electron, ion and neutral gas temperature = T e, T i, and T n, respectively dust temperature = T d dust thermal speed = v Td = (k B T d /m d ) 1/2 average neutral gas speed = v Tn = (8k B T n /πm n ) 1/2 ion atomic mass = A neutral pressure = P neutral atom density = N [m 3 ] = P [mbar] (SATP) magnetic field strength = B dust gyro-frequency = ω cd = Q d B/m d dust gyro-radius = r cd = v Td /ω cd dust-neutral collision frequency = ν dn = δ (4π/3) m n Nv Tn a 2 /m d [Epstein formula, δ~1] dust weight = F g = m d g magnetic force on dust = F m = Q d v Td B Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 6

7 Dust magnetization criteria The presence of a magnetic field strong enough to define a condition of complete magnetization for the lighter components, and sufficient to influence the dynamics of the dust, is the subject of a very small number of experiments either performed or proposed up to now. There are two criteria that must be met for a dust particle to be magnetized [Thomas Jr. et al., PPCF 2012]: r ; ω ν cd cd dn where l is the plasma dimension transverse to the magnetic field B. Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 7

8 Dust gyro-radius r cd a T 1/2 1/2 d B Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 8

9 Dust gyro-frequency / dust-neutral collision frequency ω ν cd dn B ap Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 9

10 Electron-dust system: parameters With a wall radius of a few cm, increasing B up to the order of 1 T the plasma will experience a sequence of different regimes where first electrons, then the ion fraction (when present) and finally (at least partially) the charged dust will become magnetized. Parameter Typical Values n e cm -3 B 0.9 T P mbar ρ d 2 µm R 2.25 cm V 100 V Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 10

11 The DuEl device The planned device features an internal structure of cylindrical electrodes (some of which azimuthally segmented for the excitation, control and diagnostics of plasma instabilities) and a UHV-compatible dispenser of micrometric dust, immersed in an axial magnetic field. Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 11

12 The DuEl device: CAD drawing electrode tower magnet dust dispenser thermionic electron source phosphor screen drive shaft Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 12

13 Normal-conducting solenoid magnet Courtesy of SigmaPhi Vannes (France) Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 13

14 Electron plasma generation The electrons will be generated by thermionic sources or exploiting a technique recently developed by the research group (low-power RF generation in UHV conditions by means of a few MHz-drive applied on one of the trap electrodes [Paroli et al., PSST 2010]). 320 ms 340 ms 360 ms 380 ms 400 ms The application of this technique also determines the generation of a population of ions. The latter will be adjustable by means of a controlled gas inlet as well. Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 14

15 Dust injection The dust grains will be injected into the trap by means of a rotating-drum dust-dispersal device [Xu et al., RSI 1992]. The dust is embedded in a metallic carpet fixed on the inner surface of the drum. Examples of dust grains: Silica (SiO 2, ρ d = 2.0 g/cm 3, 2a = 150 nm - 8 µm), PMMA (Polymethyl methacrylate, ρ d = 1.19 g/cm 3, 2a = 300 nm µm), PS (Polystyrene, ρ d = 1.05 g/cm 3, 2a = 100 nm µm). Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 15

16 DuEl device: diagnostics i. Optical diagnostics, based on a high resolution CCD camera and a (removable) phosphor screen, that provides the (axially integrated) transverse electron density distribution; ii. Electrostatic diagnostics, based on the recording of the time evolution of the charge induced by the plasma on azimuthally sectored electrodes, that provides information on plasma oscillation modes; iii. Langmuir probes, properly adapted to the particular conditions of operation of the apparatus (strong magnetic field, RF electric fields, presence of different charged species in the plasma) [Chen et al., PSST 2012]; iv. Optical detection of the dust by means of a self-referenced interference method of laser light scattering (Near Field Speckles), previously developed for measurements in colloidal systems [Ferri et al., PRE 2004] (able to resolve individual particles down to 100 nm with a velocity < 100 m/s). Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 16

17 Inner electrode (prototype) Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 17

18 Dust dispenser (prototype) Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 18

19 Electrode stack (prototype) Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 19

20 Numerical investigations A 2D hybrid PIC code has been developed [Maero et al., EPS 2013] in order to investigate the transverse dynamics of the electron-dust system: Discretization on a Cartesian grid, SOR Poisson solver; Multispecies, with kinetic (dust, including gravity) and mass-less fluid (electrons) descriptions; Time advancement: RK4 scheme for electrons, modified VV scheme [Spreiter & Walter, JCP 1999] for the dust grains; Fixed charge on the dust grains; Static and/or time-dependent Dirichlet conditions (circular boundary). Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 20

21 2D electron plasma / ideal fluid isomorphism ν c >> ν p >> ν bounce >(>) ν rot >> ν ee >> ν en ; R p >> λ D >> ρ e Guiding center electrostatic approximation; averaging over the bounce motion (rigid charged rods); perpendicular dynamics determined by the ExB-drift only. Note: one sign of vorticity in the electron plasma case Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 21

22 2D fluid dynamics with non-neutral plasmas The evolution of the system can be reconstructed repeating several inject/hold/dump cycles with an increasing trapping time and with the same initial conditions (injection parameters) [high shot to shot reproducibility]. t = 0 µs t = 20 µs t = 60 µs t = 140 µs Axially-integrated density of an electron plasma. The initial ring distribution is disrupted by the diocotron instability. Formation of a long-lived vortex crystal occurs. Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 23

23 Example of numerical simulation [1] t = 0.0 ms t = 0.48 ms t = 0.96 ms t = 1.44 ms The insurgence of the diocotron instability of an annular ring of electrons is slowed down by a population of of dust grains Parameters of the run: ρ d = 1.05 g/cm 3, a = 0.05 μm, Z = -100, n e = 10 7 cm -3, n d = cm -3, v y = m/s, B = 1 T, r 1 /R = 0.3, r 2 /R = (R = 2 cm, radius of the outer circular conductor), Φ (R) = 0, 256x256 grid, N e = , N d = , dt = s, t f = s. Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 24

24 Example of numerical simulation [2] t = 0.0 ms t = 0.48 ms t = 0.96 ms t = 1.44 ms Parameters of the run: ρ d = 1.05 g/cm 3, a = 0.05 μm, Z = -100, n e = 10 7 cm -3, n d = cm -3, v y = m/s, B = 1 T, R = 2 cm, radius of the outer circular conductor, Φ (R) = 0, 256x256 grid, N e = , N d = , dt = s, t f = s. Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 25

25 Numerical investigations future developments Introduction of a third species (positive ions); Discretization on a polar grid, θ-fft + FD Poisson solver; Implementation of an impedance load on the circular boundary (e.g., resistive wall); Floating charge on the dust grains; Implementation of Monte Carlo and/or particle-particle particle-mesh (PPPM) methods to describe the particle interactions (buffer-gas collision, sympathetic cooling, etc.); Development of an azimuthally-symmetric (r,z) or a three-dimensional version of the code (e.g., longitudinal-transverse plasma mode couplings). Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 28

26 Theoretical investigations The dynamics of the non-neutral complex plasma will be investigated through the analysis of the results of the numerical simulations and of the experiments. In particular, the scaling properties of electron density and velocity fluctuations will be analyzed by computing their probability densities and structure functions (detection of intermittency phenomena due to the coherent structures developed by the nonlinear dynamics of the system [Lepreti et al., PRE 2013]). The statistical and dynamical properties of the coherent structures will be studied by means of suitable data analysis techniques such as wavelets and Proper Orthogonal Decomposition. Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 29

27 2D turbulence with different ICs (electron plasma) The role and evolution of coherent structures in electron plasmas have been studied considering different types of initial conditions: annular and spiral vorticity distributions. The sequences consist of N = 250 frames with a trapping time step of 2 µs. Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 31

28 Field increments In turbulence studies the analysis of the scaling properties of the field increment statistics provides information about the presence of coherent structures, such as vortices or shocks, and about their typical spatial scales [Frisch, 1995]. u(x) r u(x+r) u() r = u(x+r) u(x) For the study of the 2D turbulence in pure electron plasmas, the scaling behavior of the vorticity increments in both x and y directions are considered: ( x ) l ( ) ( ) ( ) ( y ) ( ) ( ) ( ) Δζ x,y,t = ζ x+l,y,t ζ x,y,t Δζ x,y,t = ζ x,y +l,t ζ x,y,t l ;. Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 37

29 PDF of vorticity increments: annular case PDFs of Δζ st = (Δζ - <Δζ>)/σ(Δζ) along the x (red lines) and y (blue lines) directions for t = 2 μs, 80 μs, 240 μs, 400 μs, and for different spatial separations l. [Black curve: Gaussian PDF with zero mean and σ = 1]. The PDFs show a central core and large increment tails at all spatial separations and do not evolve significantly over time. The shape is determined by the initial condition. Lepreti et al., PRE 2013 Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 38

30 PDF of vorticity increments: spiral case The initial PDFs (t = 2 μs) are nearly Gaussian at all considered separations. Tails at large increments increase with time, especially at small scales. The deviation from the Gaussian shape increases going from large to small scales, indicating the occurrence of intermittency. Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 39

31 Flatness: annular case Structure functions are the moments of field increments, S p (l) = Δζ lp, where denotes spatial averages. A measure of the intermittency of field increments is given by the flatness F(l) = S 4 (l)/[s 2 (l)] 2 (= 3 for a Gaussian PDF). Flatness of Δζ l (x) (left) and Δζ l (y) (right) for t = 2 μs (red), 80 μs (green), 240 μs (blue), 400 μs (black). For the annular case, F(l) changes only slightly with time in agreement with the PDFs behavior. The growth of F at small scales is due to the shape of the initial condition (the drop for l < 2 mm is attributed to instrumental noise fluctuations). Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 40

32 Flatness: spiral case Flatness of Δζ l (x) (left) and Δζ l (y) (right) for t = 2 μs (red), 80 μs (green), 240 μs (blue), 400 μs (black). For the spiral case, F(l) 3 at all scales for t = 2 μs, as expected from the Gaussian shape of the PDFs. Then F(l) starts to grow going from large to small scales (down to l 1 mm) and this growth becomes stronger and stronger with time. The increase of the flatness at small scales is a signature of the intermittency arising from the turbulent dynamics of the plasma. Lepreti et al., PRE 2013 Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 41

33 Outlook The new experimental set-up (presently under construction) will offer the chance to study a non-neutral complex plasma under well-controlled conditions. In particular, it will be possible to study the dynamics of the electron plasma, its fluid instabilities and the formation of coherent structures in the presence of dust, and characterize different processes (e.g., sizing, charging, diffusion, confinement) related to the dynamics of the charged grains inside the plasma. The DuEl research project shows aspects of significant novelty in the field of complex plasmas. In particular, non-neutrality conditions of the dusty plasma and complete magnetization of all, or at least a part, of its components are aspects where a systematic investigation is still lacking. Trieste, 24/09/2013 XCIX Congresso Nazionale SIF 43