Diapositiva 1

1
THE MALMBERG-PENNING TRAP EXPERIMENTAL PARAMETERS
FIELDS OF STUDY 2D FLUID DYNAMICS, FORMATION AND
EVOLUTION OF COHERENT STRUCTURES , PLASMA MODES
Schematic of the devide
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
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
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.
Injection Hold Dump Cycle
EXPERIMENTAL PARAMETERS
COHERENT STRUCTURES IN TRAPPED PLASMAS. FREE
RELAXATION OF 2DTURBULENCE VORTEX CRYSTALS
FORMATIONS
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 Ngtgt1 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.
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
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
l1 DIOCOTRON MODE DIAGNOSTIC, INSTABILITY AND
ACTIVE CONTROL
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
(l1 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)
PERSPECTIVES... future work ...
Spectrum of the signal collected on a ?-probe

• 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 l1 diocotron mode with
  time varying ions removing fields
• Active control of the l1 instabilities with
  phase shifter and negative resistance circuits
• Active control of the l1 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 ...)

The role of the ionisation processes in
determining the l1 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.
Plasma off-axis rotation. CamV Apparatus _at_ San
Diego University (http//sdphca.ucsd.edu/mpegs)
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