Cohesive Energy Rule of Cathodic Vacuum ArcsVacuum arcs, also referred to as cathodic arcs, are high current discharges between cold electrodes. Typical currents are 100 Amperes or more while the voltage between anode and cathode is only about 20 Volts. Cathodic arc plasma is produced at cathode spots where the power density can reach 1013 W/m2. This leads to "micro-explosions," and one can observe microscopic craters left on the cathode surface. 
Crater traces left by cathode spots (Picture taken with an electron microscope) The cathode material is the feedstock material for the plasma, and therefore it is not surprising that the parameters of the plasma depend on the cathode material. Several attempts have been made to find simple relations between cathode material and plasma properties. The most successful and physically reasonable empirical rule is the Cohesive Energy Rule. It states that the burning voltage of a cathodic vacuum arc is proportional to the cohesive energy of the cathode material. The cohesive energy is defined as the energy necessary to remove an atom from the solid and to infinite distance. For a given current, I, the material-depending burning voltage, V, determines the material-depending power P=I*V. That is, material of high cohesive energy require greater power to operate the arc, or, in other words, the energy (power per unit time) invested is higher for material of greater cohesive energy. Examples of materials with high cohesive energy are W, Mo, Ta, and examples of low cohesive energy are Bi and Pb. As a result of this energy-based rule, one can find a number of secondary rules for ion charge distributions, ion velocity distributions, and ion erosion rates. Measurements for these parameters are briefly summarized here. Publication highlight: A. Anders, "Cohesive energy rule for vacuum arcs," in: Emerging Applications of Vacuum-Arc-Produced Plasma, Ion and Electron Beams, NATO Science Series II. Mathematics, Physics and Chemistry vol. 88, I. Brown and E. Oks, Eds. Dordrecht: Kluwer Academic Publishers, 2002, pp. 1-14. Ion Charge State DistributionsOne of our main contributions to the field of vacuum arc plasma physics was the investigation of ion charge state distributions. Starting in the late 1980s, we measured the ion charge state distributions by coupling our vacuum arc ion source "Mevva" with a home-made time-of-flight spectrometer. By improving the spectrometer and adding features to the arc plasma generator, we were able to determine charge state distributions for over 50 cathode materials and study the effect of magnetic fields and the time evolution of the distributions. In the Table below, a number of parameters are compiled for many cathode materials, including the Cohesive energy, the displacement energy, burning voltage at 300 A, kinetic energy, ion charge states (particle fractions), and ionization energies for selected cathodic arc plasmas. The burning voltage, kinetic energies, and ion charge state distributions are values averaged over many discharges, thereby not showing the fluctuating nature of these values. The ionization energies are conventionally defined as E0 for the energy to ionize the neutral, E1 to remove an electron from the singly charged ion forming a doubly charged, etc.
For more details, see A. Anders, "Energetic deposition
using filtered cathodic arc plasmas," Vacuum, vol. 67, pp. 673-686, 2002. Other publication highlights:
Ion VelocitiesIons can achieve surprisingly high velocity which is generally of the order 104 m/s. The corresponding average kinetic energy Ekin=mv2/2 is between 19 eV (carbon) at the low end and 160 eV (uranium) at the high end. Kinetic energies are also included in the table above. The cohesive energy is again a good orientation for the energy than one can expect. This is not coincidental because the ion acceleration is associated with pressure gradients of the cathode spot vicinity. The more energy is pumped into the system, the greater is the kinetic energy observed. Modified time-of-flight methods have allowed us to determine not only the average ion energies but their distribution functions.   Carbon and Platinum ion velocity distributions measured for pulsed arcs. The functions do depend on the arc pulse repetition rate. The precision of the method is smaller the higher the velocity, hence the oscillations at the high-velocity end are artifacts of the measurements. The carbon and platinum velocity distributions are examples that show that there is only one major peak in the distribution, with a HWFM (half-width-at-full maximum) that is rather narrow. It indicates that all ions have about the same velocity distribution, as opposed to a velocity distribution that is proportional to the ion charge state. This indicates the dominance of a hydrodynamic nature of acceleration. Measurements with an electrostatic energy analyzer of plasma from a magnetically "steered arc" give somewhat different results, indicating that acceleration by an electric field may not be neglected. Publication highlights:
Ion erosion ratesThe cathode is eroded in the process of cathodic arc operation: plasma is produced form the material, which enables us to use the system for coatings. On can distinguish between material in form of ions and in form of microscopic droplets, so-called "macroparticles." The ion erosion rate is the "useable" component for high-quality coatings. Measurements show that the higher the cohesive energy, the lower the ion erosion rate. That is not surprising because the cohesive energy is a measure for the energy needed to transfer material from the solid to other phases. Table: ion current (ai, in percent, normalized by the arc current), and ion erosion rate, gi, measured in μg/C for selected cathode materials.
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MacroparticlesThe other important form of cathode erosion is via microscopic droplets or "macroparticles." The term "macroparticle" is used to emphasize the massive nature of the particles compared to plasma particles (electrons and ions). Macroparticles are highly undesirable for the formation of high quality coatings. Therefore, a number of techniques is applied to reduce macroparticle formation and to remove macroparticles from the plasma via filtering. Here, we studied the velocity and size distribution of macroparticles. In the literature, it is often quoted that the size in the range 0.1 mm - 10 mm. On the large end, the size is accociated with the limited crater volume that is observed. On the small end, the size is associated with instrument resolution rather than a physical cutoff. Measurement with higher resolution have shown that macroparticles smaller than 100 nm can be found. The size distribution follows a power law and is one of the arguments for the fractal nature of cathode spot phenomena. 
Macroparticle size distribution for copper arcs. This graph contains data obtained by the Plasma Applications Group supplemented by data courtesy of Peter Siemroth, Dresden, Germany. Publication highlights:
See also Publications
Fractal ModelModeling cathodic arcs has been a challenge for decades which is due to the small scale of spot process (~ micrometers) and the short times of arc spot ignition processes (~ nanoseconds). Studies of the fluctuations aimed to identify characteristic scale and times but the general result was that the greater the resolution the finer were the structures in space and time. Accordingly, there was and is debate on the fundamental mechanism and governing parameters, especially the current density. The situation is not unlike the now-familiar question: What is the costal length of Great Britain? Due to many research in fractal physics, and the brilliant interpretations by researchers like Benoit Mandelbrot, we know that the answer is related to the scale length of measurement, until one reaches cutoff limits (elementary processes) in physical system. Self-similarity and associated power laws are abundant in cathode spot phenomena, including optical appearance, the shape of arc traces, the power laws in macroparticle distributions, the power laws found in noise distributions of the fluctuating parameters. For example, the noise of arc burning voltage shows a characteristic 1/f2 dependence, which is known as "brown noise." With this interpretation one can recognize that parameters like the current density should not be expressed by a single number but described as a fractal. This approach allows to consolidate various other models such as a cathode layer model and the explosive emission model. Cathode spot phenomena are fractals in space and time. 
Spectral amplitude of voltage noise for a magnesium arc. The spectral amplitude was obtained by Fast Fourier Transform (FFT). The amplitude scales with 1/f, and the corresponding spectral power by 1/f2, which is characteristic for brown noise. Publications highlights:
For more information, contact André Anders. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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