Like Faraday’s “The chemical history of a candle”, electric arcs have been studied extensively and recorded in Hertha Ayerton’s “The Electric Arc” (Which I obviously haven’t read because I am supposed to be studying propulsion) . This is partly due to their applications in various fields but mostly because they look (and sound) cool. The formation of an arc proceeds through the electric breakdown of the gas in which they operate (the propellant in our case). High voltages cause thermionic emission of electrons from the electrodes which ionise the propellant, heating it to the high temperatures required in an electrothermal thruster. Like all circuit elements, arcs have their own voltage-current characteristic and it’s a good idea to discuss it here.
The graph is divided into various regions, each with their own properties.
In region O-A, the voltage is small and the electric field just collects the stray charges (mostly electrons) created by other sources (like cosmic rays). Region A-B is called the first Townsend region and it is where the stray electrons acquire enough energy to ionise other atoms by collision. Region B-C, the second Townsend region, is where even the positive ions acquire enough energy to knock out electrons from the cathode by bombardment.
The dotted line at C-D indicates something interesting. This is where the discharge becomes momentarily unstable and the arc switches to a new lower voltage mode. The voltage Vc is called the sparking potential. Beyond C, a normal discharge called a glow discharge sets up which, while having no practical applications in propulsion, looks pretty.
The region F-G is where practically interesting things happen, the voltage near the cathode drops abruptly and a new type of discharge called an arc discharge develops. This discharge’s resistance drops rapidly as the voltage is changed, hence a ballast resistor is needed to protect the electrode from vaporisation. Ionisation is now vigorous with electrons flowing from the cathode to the anode and the propellant ions the other way. This is where the fun starts !
Now people might ask,
“You wanted high temperature not in contact with the metal, what about the electrodes.”
Well, all arcs have a profile that tells how a property changes along it’s length. A typical arc profile is given below.
The positive column is where the most thermally excited particles are found. Temperature here can range anywhere between 5000 to 50,000 K depending on the current. So, now you have a way to heat the propellant to a much higher temperature than the melting point of the thruster body. The core of the propellant column can now be made much hotter than the part that touches the thruster directly thus greatly enhancing the exhaust speed. Good going !
In spirit of theoretical physics around the world, let us assume the arc to be a uniform cylinder. One of the various hand rules thought in your school will tell you that the magnetic field lines around the arc are in the form of concentric circles centred on the axis of the arc. This magnetic (self) field applies a force on the current that creates it, pushing the particles inwards. This is where things go wrong.
If the magnetic force exceeds the gas-kinetic pressure on the inside of the arc, the arcs starts contracting at the point where this happens. This is called pinching. Pinching is more adverse if the arc is allowed to bend. Bending (or kinking) increases the magnetic field on the concave side of the bend leading to even more pinching. (see diagram)
Pinching might lead to the breaking of the arc which is not a good thing considering the whole damned process we underwent to get an arc discharge. It’s a good idea to try to alleviate these problems while designing the thruster. This is usually done in two ways,
- Vortex stabilization, where the propellant is injected into the thruster tangentially to the arc. This induces a spin and prevents both kinking and pinching by stabilising it centrifugally.
- Constriction, where the arc is constricted to a small space so that it can’t bend. These techniques are almost always used together for maximum efficiency.
A typical thruster
The complete design of a 30-kw arcjet thruster is given in the diagrams below along with the operating conditions.
As can be seen in the last diagram above, the arc culminates in a spread over the anode nozzle. This also gives rise to a destabilisation problem.
The part where the arc attaches to the anode is quite creatively called the “anode attachment”. To prevent erosion of the anode, it must be spread symmetrically over the whole circular cross section . If the attachment is to collapse into a single spoke even for a second, it would mean the end of the anode due to high concentration of kinetic particles. An axial magnetic field is generally used to prevent this from happening. The magnetic field forces the particles to spread out uniformly over the cross section as they spiral along the field lines.
This was the basic breakdown of how arcjets work and the problems they face. As is seen in the thruster characteristic table, these are much more efficient than resistojets due to higher exhaust speeds. Frozen flow losses do exist but the efficiency of the thruster makes up for them.
Both of these thruster discussed use electricity to heat the propellant. However, there are better ways to gain high exhaust speeds without thermodynamics coming for the rescue.
So, I’ll leave ion thrusters for the next article.
Merry Christmas !
 Robert G. Jahn “Physics of Electric Propulsion”