Free Plasma Expansion with Double Layer Formation

The free expansion of plasma into vacuum is a topic of interest to space plasmas and laser produced plasmas. The main point of interest is the continuous acceleration of ions at the expansion front where a space charge electric field is set up by the faster electrons. The expansion front is essentially a moving sheath where the ions are accelerated on expense of the electron energy.

We have studied the free expansion of a pulsed magnetized discharge plasma containing two populations of electrons, a cold Maxwellian and an energetic shell of primary discharge electrons. A weak magnetic field confines the electrons radially which results in a preferentially axial plasma expansion. Neutral gas is puffed radially into the discharge source thereby achieving a plasma expansion into vacuum. The basic parameters for the experiment are listed in the table of Fig. 1b

Experimental setup and basic parameters

Fig. 1 (a) Experimental setup in the plasma device. (b) Basic parameters for the experiment.

The measurement of the plasma potential is vital to understanding the expansion physics. The main diagnostic tool is an emissive probe whose floating potential is close to the plasma potential if the emission current balances the electron saturation current. The potential has to be measured with a high impedance voltage follower. In order to obtain a microsecond time resolution the probe capacitance has to be minimized, which is accomplished by switching the heater power supply off during the short plasma expansion phase. With these precautions the time development of the axial plasma potential profile is obtained and shown in Fig. 2a.

PotentialMeasmt

Fig. 2. Plasma potential measurement and its diagnostic tool. (a) Axial potential profile at different times of the free plasma expansion. The initially continuous potential drop develops into a stationary double layer. (b) The potential is measured with an emissive probe. During the measurement the heater supply is switched off so as to reduce capacitive loading which results in a fast time response with a high impedance voltage divider and buffer.

Initially the large potential drop is determined by the energetic 80 eV discharge electrons. As the ions are accelerated the free sheath expands. Those which reach the front gain the full energy of the primary electrons. They continue to be accelerated to even higher energies when they are traveling with with increasing time a second feature develops. It is a sharp potential drop which becomes stationary, known as a double layer. Its potential drop is large enough to reflect all secondary electrons but it passes the energetic electrons and accelerates ions. It forms where the potential drop of the primary electrons is large enough to reflect the secondary electrons. The expansion continues but is driven by the energetic electrons while the cold electrons are confined by the double layer. The stationary double layer is current-free since ions and primary electrons pass it at the same rate. The formation of a continuous ion beam is unrelated to the ion acceleration at the expansion front.

Figure 3 shows the different particle energies during the free plasma expansion. The electron temperature, measured by a Langmuir probe and plotted in Fig. 3a, shows an axial increase as the plasma potential drops. Only tail electrons reach the expansion front. The ion energy, measured with an energy analyzer also increases axially. As the ions are accelerated the density decreases to conserve the particle flux of the plasma stream. Only few ions reach the highest energy at the expansion front.

Plasma potential

Fig. 3. Electron and ion energies and density profile. (a) The electron energy decreases along the axial potential drop. Only energetic electrons reach the expansion front. (b) Axial density profile and ion energy. As the ions are accelerated their density drops so as to conserve the flux. Ions at the expansion front reach energies exceeding that of the electrons.

Figure 4 displays the properties of the double layer. Potential measurements are extended to two dimensions (Fig. 4a) showing that the double layer has the width of the expanding plasma column. Along the axis Fig. 4b shows the potential and its derivatives, i.e. electric field and two space charges of opposite sign, hence a double layer.

Plasma potential contours displaying double layer

Fig. 4 Double layer properties. (a) 2D potential contours showing the location of the double layer in the middle. The density profile is indicated in the right panel. (b) Properties of the double layer, showing the axial potential profile, the electric field and space charge density.

Finally, Fig. 5 shows another feature of the expansion process which has not yet been fully explained. On the downstream region of the double layer significant low frequency density and potential fluctuations are observed (Fig. 5a). Their spectrum falls into the ion acoustic frequency regime (Fig. 5b). Two-probe cross correlation measurements show that the oscillations propagate, not surprisingly along the expansion direction (Fig. 5c). A plot of frequency vs inverse wavelength show a straight-line dispersion relation with a phase velocity well exceeding the sound speed (Fig. 5d). It can be interpreted as sound waves riding on an ion flow. The latter is the ion beam from the double layer. The mechanism of the instability has not been identified but may lie in an instability of the free double layer from where the waves originate.

Plasma potential contours displaying double layer

Fig. 5 Fluctuations observed during the free plasma expansion. (a) Density and potential waveforms downstream of the double layer. (b) The frequency spectrum of the fluctuations falls into the range of ion acoustic waves. (c) Cross-spectral measurements show the direction and speed of wave propagation. (d) Dispersion relation of the waves reveal a supersonic propagation speed due to the rapid expansion of the ions.

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