Joseph Chikva wrote:
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And Dan is wrong for example when says that Debye length is defined only for static systems.
If so please explain how solar wind with typical value of Debye length 10 m we can cosider as static?
And so on.
Also for reference at 10^22 m^-3 number density plasma in Polywell will have about 10^-6 m Debye length. So, order of magnitude of charge separation will be equal to 10^-5 m = 0.01 mm. Now understand?
First, you second point, I'm uncertain of your assertion. The Debye length is dependent on the density, but also the temperature. For convenience consider the Polywell as operating at 10 X the average temperature of a Tokamak. So if you are using that as your baseline you need to adjust.
Debye length and shielding are widely used in plasma physics ionics in general. Capacitor behavior, plasma behavior, etc. are usefully represented by this parameter. The definition of the Debye length is dependent on mobile charge carriers and the difference in their mobility (speed Any current flow atomic nuclei are not.- in effect the ion) Thus a potential results in a flow of electrons only (ignore concepts like holes or plasmons that are used to explain some processes). In a plasma the ions can move and this changes things in some ways, but still the lighter/ faster electrons determine the build up of charge separation. And at some point this charge separation will result in opposing electrical fields that counteracts the potential on a fixed electrode (fixed in space or time) and the initial current flow (redistribution of mobile charge carriers) stops and a new equilibrium is established. This is where my uncertainty and belligerence enter the picture. The Debye length is an equilibrium state, which means there is no input or output of energy in the system. Things change when there is an outside influence, such as an applied electrical bias, either via a fixed electrode or by introduction of an excess of negative or positive charge carriers. The system is again in a non equalibrium state and current flow will occur until a new equilibrium is established. If input is maintained the equilibrium will never be reached and current flow will be continuous through the system (in one side and out the other).
Statements that Debye shielding prevents current flow is miss leading. This only occurs in the static or equilibrium condition. Static means unchanging- which means no current flow through the system. Debye length/ shielding is a static consequence of mobile charge distribution. It describes the distance at which an unbalanced charge will communicate in a static time frame (or a zero system current frame (actually time of the speed of light considerations)). This is useful for describing the scale of influence of local charge imbalance in an larger plasma or other substrate - the limits that a local charge imbalance can exist- such as islands of charge separation in an overall neutral plasma.
These interactions applies to many systems, not just plasmas. Take a liquid salt solution. The ions will mix together through well defined processes till they are evenly distributed (in equilibrium). The solution is neutral both globally and locally (at scales greater than a few times the average ion separations). There might be local variations that arise due to random/ chaotic behavior, but the maximum extent of these are limited by Debye shielding in the system. Again this reflects the solution at equilibrium- a closed system. The kicker is when the system is influenced by an external force- a potential applied by electrodes. The ions start moving dependent on the potential and their mobility. The lighter ions will move faster and this sets up the Debye length relationship. This imbalance is a temporary though. The ions will continue to redistribute (the system is perturbed) until the potential applied to one side of the system reaches the other side and there will be net flow of current through the entire system. Statements that suggest this will not occur if the distance is greater than the Debye length is what annoys me. It is just nonsense.
Of course the Debye length is involved with a lot of behavior in a plasma, gas, liquid, or solid. It is tied to other parameters like plasma frequency, conductivity, density, temperature, etc. But this static definition being applied to dynamic situations (non equilibrium) without consideration of modifications is inappropriate.
In the Polywell, if you consider Gauss Law simply, then any electrons inside the radius of the ion will have a net attraction on the ion, while those electrons outside the ions radius will not have a net attraction because they all cancel out. If you apply the static Debye shielding distance, then only those electrons within this local radius will effect the ion. This limits things and changes the ion acceleration characteristics. But this ignores the electrons beyond the Debye shielding distance to the ion, but within this distance to other electrons, or ions. Thus this electron is moving due to influences of the test ion and any other ions or electrons within it's specific Debye shielding distance. Thus indirectly, electrons (and ions) at distances greater than the Debye length are effecting the test ion. Since this interaction is dependent on interactive motions, it is time dependent, so of course temperature and other plasma motion and collision perimeters apply. It is a complicated picture but directly or INDIRECTLY every electron effects every ion, not only those within the Debye length of that electron. If the system is closed- in equilibrium things settle down until the distributions become static- defined quasi neutral definitions, etc. But so long as there is a potential applied (represented here by the excess energetic electron injection) things remain dynamic and equilibrium is never reached.
In effect (at least in my mind) the potential well is a global thing, made up of many local Debye length dependent interactions, but still overall a global process, much like the current conducted though a salt solution due to the potential between two distant fixed electrodes.
The mention of the time dependance/ current dependance upon the Debye length definition and its significance are hard to find but some hints may be found in these links:
http://www.tf.uni-kiel.de/matwis/amat/e ... 2_4_2.html
http://www.google.com/url?sa=t&rct=j&q= ... V8hpNNPzrw
Dan Tibbets
To error is human... and I'm very human.