Congresso del Dipartimento di Fisica

Highlights in Physics 200511–14 October 2005, Dipartimento di Fisica, Università di Milano

Coherent structures and diocotron instability in electron plasmasG. Bettega*†, F. Cavaliere*, M. Cavenago+, F. De Luca*†, D.Ghezzi*°, A. Illiberi*†, R. Pozzoli*†, and M. Romé*†

* Dipartimento di Fisica, Università di Milano† INFN, sezione di Milano + INFN, Laboratori Nazionali di Legnaro °Politecnico di Milano

THE MALMBERG-PENNING TRAP: EXPERIMENTAL PARAMETERS

Injection Hold Dump Cycle

Schematic of the devide

Plasma off-axis rotation. CamV Apparatus @ San Diego University (

http://sdphca.ucsd.edu/mpegs)

The diocotron modes can be also diagnosed by passive, non desctructive methods, collecting the induced charge signals which forms on the electrodes of two aximuthally sectored cylinders. The small voltage signals are amplified and conditioned, then acquired and sofware processed by a LabVIEW virtual instrument: their spectra give informations about the frequencies and the amplitudes of the waves. The fundamental wave (l=1 diocotron mode) - which is equivalent to an off-axis plasma rotation is predicted - stable by the theory, but is found UNSTABLE in the experiments: the plasma is driven towards the wall (curve -a-, free evolution of the instability)

COHERENT STRUCTURES IN TRAPPED PLASMAS. FREE RELAXATION OF 2DTURBULENCE: VORTEX CRYSTALS FORMATIONS

Spectrum of the signal collected on a -probe

When the field are applied the ions are ejected out of the plasma confinement volume and the instability is removed.

Compare the evolutions in the graph ...

(a) free evolution of the instability

(b) ions removal from 1s to 2s

(c) ions removal from 2s to 3s

Ions removing fields

FIELDS OF STUDY: 2D FLUID DYNAMICS, FORMATION AND EVOLUTION OF COHERENT STRUCTURES , PLASMA MODES

The role of the ionisation processes in determining the l=1 diocotron mode instability has been recently evidenced: the application of proper “ions removing field” has been succesful in controlling the increase the instabilty: the use of this techique allows to double the lifetime of the plasma.

A trapped particle axially oscillates at a frequency much larger than the ExB motion one: on this “slow” time scale it is equivalent to a rigid charged rod undergoing a pure ExB (therefore incompressible) motion (“point vortex”). The whole plasma behaves 2D (cold) fluid whose dynamics is well modeled by the Euler equations for an ideal (not compressible, inviscid) classic fluid

The plasma is axially trapped within a potential well created by two negative voltages; the radial confinement is obtained by the application of an axial magnetic field which keeps the plasma in rotation around its axis: the JxB electrodynamical force which generates is inward directed and balances the electrostatic repulsion bteween the particles

EXPERIMENTAL PARAMETERS

FORMATION OF 2D VORTICES

A small initial density perturbation, present as a noise on a ring shaped plasma, propagates azimuthally on its surface, exponentially growing in time and driving the dynamics in a strongly non linear regime. This kind of instability, known as Diocotron Instability, is analogous to the well known Kelvin-Helmoholtz instability of the fluid with shear flow. The initial phase of a trapped plasma evolution (~100 ms) is characterised by the formation, the interaction and the dissipation of small 2D vortices as long as a smooth radial equilibrium is reached.

The plasma is generated by a thermionic spirally shaped cathode, so the initial density distribution reflects the shape of the source. Such an initial density diatribution is strongly unstable and becomes turbulent: N>>1 vortices (electron columns) form, which non linerarly interact through merger events and originate filaments of low electron density. The number of vortices decreases in time towards a single vortex state according to a power law

For some source parameters the free relaxation of the initial turbulence is halted and a VORTEX CRYSTALS state forms, made of a stable rotating arrays of vortices. The measured number of vortices versus time abandones the power law and forms a plateau.

Once formed the vortex crystal states last for thousands of bulk plasma rotation and are finally dissipated by the non zero viscosity. The relationship between the initial conditions (source and injection parameters) and the formation of a vortex crystal is not well understood

The self organisation properties of the 2D turbulence are investigated within the context of variational methods (maximisation of entrophy, minimisation of enstrophy, RMFE – Regional Maximum Fluid Entrophy -). Similar vortices structures are also observed in many natural occuring flows (hurricanes, the Great Sopt on Jupiter) which can be modeled as two dimensional; the similarity between 2D vortices interactions and galaxies merger is striking

l=1 DIOCOTRON MODE: DIAGNOSTIC, INSTABILITY AND ACTIVE CONTROL

PERSPECTIVES... future work ...

EXPERIMENTS ON 2D COHERENT STRUCTURES IN TRAPPED PLASMAS AND IN LOW ENERGY ELECTRON BEAMS

➢Extended experimental scanning of the initial conditions originating monotonicaly decreasing sequences of vortices and vortex crystal states

➢Application of the super-resolution techique (wavelet transform) to the acquired images in order smaller 2D coherent structures

➢2D Turbulence spectra (fluctuations, cross correlations of relevant quantities, energy spectrum, vortices cascades)

MANIPULATION OF PLASMA MODES WITH EXTERNAL CIRCUITS

➢Active control of the l=1 diocotron mode with time varying ions removing fields

➢Active control of the l=1 instabilities with phase shifter and negative resistance circuits

➢Active control of the l=1 diocotron using external resonant (LC) networks

HIGH FREQUENCY ELECTROSTATIC DIAGNOSTIC SET UP

➢Set up of the electrostatic diagnostic for the plasma high frequency modes of oscillation (amplification, filtering, interfacing ...)