10−1 100 101 102 102
103
pd (Torr−cm) V b(V)
Ne
He
H2 N2
Ar
Figure 1.10: Paschen curves calculated from Eq. 1.30. The curves give the minimum DC voltage for breakdown of each gas as a function of pd. γse= 0.07 was assumed [44]. These curves are only rough estimates; in reality A and B in Eq. 1.30 are only constant over a limited range of electric field strengths, and γse is also energy-dependent above∼500 eV, so experimentally obtained Paschen curves will be more accurate.
whereγseis the secondary electron emission coefficient for ions striking the cathode and A andB are empirically determined constants. Using values forAandB from [5, Table 14.1], Eq. 1.30 is plotted in Fig. 1.10 for several gases of interest.
The dependence onpdmay be understood intuitively by realizing that breakdown occurs through electric impact ionization of neutral atoms. The mean free path for electron-atom collisions isλen= (ngσen)−1, wherengis the gas density andσenis the collision cross section.
Ifpdis very small, then λen will be longer than the inter-electrode distanced, and too few ionizing collisions will occur to achieve breakdown. On the other hand, ifpdis too large,λen will be very short compared to d, and electrons will tend to undergo randomizing collisions before they have been accelerated through a sufficient potential difference to attain the energy necessary for ionization. Breakdown is thus easiest to achieve at intermediate values ofpd. Below a thresholdpdat which the Paschen curve asymptotes to vertical, breakdown is not possible at any voltage. The Caltech experiments have typically operated near this low- pressure limit for breakdown, at the left-hand side of the Paschen curve. Therefore, unless the distance between the electrodes was increased, which was not practical, the quantity of gas injected (which ultimately determined the plasma density since the discharges were
nearly 100% ionized) could not be decreased.
However, if plasma is already present when a DC electric field is applied to a system, then the Paschen breakdown criterion does not apply. It is easier to sustain a gas discharge than it is to initiate one. The rest of this thesis describes the design and characterization of a radiofrequency (RF) pre-ionization system, and its application to the Caltech experiments.
By ionizing plasma in a tube behind the electrodes and allowing it to flow into the chamber before the main capacitor bank was triggered, it was possible to make lighter, faster, hotter MHD-driven jets than could be created using Paschen breakdown alone. Independent of the pulsed power jet experiment, some interesting RF discharge behaviors were discovered and studied in detail—these investigations are the subject of Chapters 3, 4, and 5.
Chapter 2
Pre-Ionization System Design
2.1 RF Plasmas
Various technologies for achieving plasma pre-ionization exist, including triggered spark gaps, hot electron-emitting filaments, radiofrequency (RF) plasma sources, and microwave sources. Microwaves with frequency∼100 GHz have been used in many tokamaks to assist in start-up through electron cyclotron heating (ECH), and this method is planned for ITER [46, 47, 48]. RF pre-ionization has been used at the HIT-SI spheromak experiment at the University of Washington to achieve lower plasma densities [49], and also in tokamaks [50].
For the Caltech experiments, RF pre-ionization was chosen due to the modest cost and scale of the apparatus needed and the promise of high ionization efficiency with relatively low input power. Since the plasma density in the original MHD-driven jet experiment was around 1021–1022m−3, the pre-ionization plasma source needed to be able to produce plasma with density on the order of 1017–1020 m−3 in order to access an interesting new experimental regime. This density range is readily accessible in RF plasma sources with
∼1 kW of input power [51, 52, 53].
Three means of transferring energy from an RF power source to a plasma exist: capac- itive coupling, in which a large amplitude oscillatory voltage on an antenna or electrode creates a high voltage sheath at the edge of the plasma, driving RF currents that heat the plasma; inductive coupling, in which a time-varying current through an external coil or antenna induces electric fields which accelerate electrons in the plasma; and wave heating, in which waves excited by an antenna are damped and transfer their energy to the plasma as they propagate through it or along its surface [5]. Each type of RF discharge has impor- tant applications in the fabrication of integrated circuits (plasma processing) and for other
27.12 MHz Oscillator
Antenna Capacitive matching
network Transformer Logic
modules
DRF1301 MOSFET Push-Pull
Module
Gating Pulse 300 V in
RF Amplifier
13.56 MHz output UV Lamp
Fast Gas Valve Quartz Tube
Solenoid Alternating 13.56 MHz trigger pulses
Figure 2.1: Block diagram for the RF plasma source, showing the main sections of the RF amplifier and the other key components described in the text.
surface processing of materials used in industry [5]. Usually a plasma source is designed to take advantage of a particular energy transfer mechanism, but in some cases all three coupling regimes have been observed in a single device as the RF input power was varied [54].
A particular class of wave heated discharges that operates with helicon waves has been found to be exceptionally efficient at producing a high plasma density with low input power [51]. The impressive properties of helicon sources [55, 56] made them an attractive candidate to use for pre-ionization in the Caltech experiments, so we designed our RF plasma source with helicon mode operation in mind. However, detailed density scaling measurements (described in Chapter 3) ultimately showed that wave heating was probably not important in our source; instead, the discharge was found to be primarily inductively coupled.