My Attempt to Explain Biased probes

[mattman]

Hello all,

In the newest work from Joe Khachan, (Physics of Plasma 5/9/2013) they stuck metal probes inside the plasma in a polywell. They put a bias on these probes. As the plasma touched the probes, a current was gathered. From this, they measured things like, the electron energy and density.

Below is an attempt to explain how a biased probe works and how they set up the probe. It’s still very rough! This was put together after reading some papers and technical literature. PLEASE RIP THIS EXPLAINATION APART. There are probably mistakes here.

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Steps to install a biased probe in Sydney experiment:

1. First, estimate the Debye length for the plasma. This is the maximum distance over which a particle can interact with another particle. If particle B is outside the Debye length, particle A cannot “see” it. Particle A cannot kinetically or electrostatically interact with particle B; not directly. This is the equation I have for the Debye length.



2. For the probe to work and be understandable, the sizes must follow certain rules. These rules dictate the fixed size of the device and probe. These sizes bound the Debye length. This, in turn bounds the types of plasmas used. If the Debye length is longer than the probe it will create small problems. This did occur in the paper.



3. The probe is a long thin tungsten wire. This is placed in the plasma. This wire is 8 to 15 degrees off the magnetic field lines. The probe is placed - on purpose - so that plasma will touch it. Normally, the magnetic fields designed so plasma will avoid touching metal. Probes do the opposite.



4. The plasma’s random motion means some of it will touch the probe. Hence, the metal is taking in positive and negative charges. This signal tells you very little. Much more information can be extracted when a bias is applied. The signal will go highly negative or positive if excess charge is present. This is how - in their 2010 paper - they proved that the Polywell was trapping electrons.



5. A voltage is applied to the probe. This makes the wire is biased negative against the plasma. Therefore a negative charge is repelled. A sheath of plasma forms around the wire.



6. This applied voltage is varied with time. The probe will “sweep” across various ranges.



7. This changes the voltage across the sheath. As the voltage changes, electrons with different energies can touch the probe. This is shown below.



8. The signal coming from the probe can be interpreted for various bits of information. This signal is called the IV curve. The energy and density of the ions and electrons can be pulled from this information.



Much of this info was from:
http://impedans.com/langmuir-probe.html

[D Tibbets]

I'll interject some of my understanding of the Debye length. Based onb my reading the Debye length is defined by setting up a situation where there is current transfer, but an infinitely small current. If there was no current the situation would be static and the Debye length would be undefined. If there is more than an almost infinitely small current, again the Debye definition becomes meaningless. It is this very narrow definition that confounds my understanding when it is applied to dynamic situations. The Debye length/ shielding occurs because electrons have less inertia than ions, so when exposed to a fixed point potential, they will start moving faster than the ions. This creates a charge separation which 'shields the fixed electrode from charged particles further away than som distance as defined by the Debye length. This is fine, but what happens when charge separation is changing on time scales/ current amounts that are not in the Debye definition. Things becomes blurred. The electrode is shielded, but the electron halfway to the Debye length still sees the charge on the electrode, and also the charges on all of the charged particles within a Dbye length of itself. Charged particle motions would shift accordingly. Essentially there are an almost infinite number of Debye lengths that overlap. Thus a charged particle will eventually see the potential that was introduced into the system. It is a question of time. At high currents the time delay for the effect of the unbalanced potential to extend across the plasma is short, at tiny currents the time is long. At almost infinitely small currents the Debye length is limiting the potential imbalance communication distance and this approximation applies only if the current is infinitely small or the time slice is infinitely small. Obviously, a plasma is a conductor and current will pass through it even at distances much greater than the Debye length. It is this static verses dynamic picture that gives me problems with some of the plasma characterizations. I know that this Debye relationship is involved in a lot of calculations, but again the dynamic evolution of the charge separation/ potential across the plasma is an iterative process that changes with time (unless the charge flow is infinitely small). This ties in with various concepts like global neutrality or not and quasi neutrality limits.


One small adjustment to your formula. The Temperature in a thermalized plasma is a range following Maxwell Boltzman distributions. Thus the Debye Length definition results in a range. I believe this is why Debye shielding is often referred to as plus or minus some average. Something like the statement: 'the charged particles do not see a potential located further away than 1-2 Debye lengths (calculated from the average temperature)'. In a Polywell, this range would presumably be less because the plasma is not thermalized fully. The temperature variation is more closely clustered about the average temperature.

Note that in a Tokamak with charged particle confinement times of hundreds of seconds, at a given density and volume, the the flow of current (escaping charged particles) across a barrier (or some other measured locale) represents a far smaller current than in a Polywell where the confinement time is measured in milliseconds and the density is higher. The current difference under similar conditions may be by a factor of ~ 1 million. As such, an almost statically defined Debye length is much closer to the dynamic situation in a Tokamak verses a Polywell. How this effects things is a question that is beyond my pay grade, though it would seem to require very careful interpretation of predictions based on the Debye length without modification.

Dan Tibbets