![QUANTITATIVE
EXPRESSION FOR DEBYE
SCREENING
To temperature , the thickness of charge cloud
let the potential ф on the plane x=0
is held at a value ф0 by perfect transparent gain.
To compute→
ф(x) assume that the ion electron mass ratio M/m is infinite
So ions do not move but from uniform background of +ve charge.
We can say that M/m is large enough that the inertia of the ion prevents them from moving
significantly on the time scale of the experiment.
Poisson ‘s eqn → Ԑ0∇2Ф= Ԑ0∂2ф/∂x2= -(eni-ne) (z=1)
If the density for away is n∞, we have ni= n∞
In present of a potential energy qф, the electron distribution function is
F(u)= A exp[-{(mu2/2)+(qф)}/kTe]
Te= temperature of electron](https://image.slidesharecdn.com/helly-200923095240/85/QUANTITIVE-EXPRESSION-FOR-DEBYE-SCREENING-AND-QUASINEUTRAL-PLASMA-8-320.jpg)
QUANTITIVE EXPRESSION FOR DEBYE SCREENING AND QUASINEUTRAL PLASMA
- 2. QUANTITIVE EXPRESSION FOR DEBYE SCREENING AND QUASINEUTRAL PLASMA CCE - I
- 3. “ A plasma is a quasineutral gas of charge and neutral particles which exhibits collective behavior “ In plasma charged particle are present as these charge move around they can generate local concentration of +ve or – ve charge which give rise to electric field. Motion of charges generate current & hence magnetic fields. These fields affect the motion of other charged particles for away. DEFINITION OF PLASMA
- 4. DEBYE SHIELDING A fundamental characteristic of the behavior of the plasma is the ability to shield potential that are applied to it. Plasma are ionized gases which are electrically conducting by virtue of their charged particle but they are electrically neutral because the no. of positive charges and the no. of –ve charges balance each other. Electron lighter charges contribute to current. Ions heaver scenes to neutralized the plasma. Due to charge neutralized electrostatic force can be ignored.
- 5. DEBYE SCREENING DISTANC If a plasma is subjected to an internal electrical field ,say by introducing a charge in it. The charge carriers rapidly distribute in such a way that most of the plasma is shielded from the field. The distance in which the effect of introduced charge is screened out is called Debye screening distance. Suppose put electric field inside a plasma by inserting two charged ball. Balls would attract particles of opposite charge and almost immediately a could of ions would surround the balls. For cold plasma no. thermal motion there would be just as many charges in the cloud as in the ball, shielding would be perfect and no. electrical field would be present in the body of plasma out side of the clouds. If the temp. is finit,those particle that are at the edge of the cloud where the electric field is weak have enough thermal energy to escope from the electrostatic potential well the “edge of the cloud then occurs at the
- 6. QUASINEUTRALITY If the dimension L of the system must large than λd. The whenever local concentration of charge arise or external potentials are introduced into the system L>> λd then system are shielded out in a distance short compared with L, leaving bulk of the plasma free of large electric potential or field Outside of the sheath on wall ∇2Ф→ very small & ni=ne It takes only small charge imbalance to give rise to potential of order of kT/e.
- 7. QUASINEUTRAL PLASMA Neutral enough so that one can take hi≈ he≈ h Where n is common density called plasma Density. Not so neutral that all electromagnetic force vanish.
- 8. QUANTITATIVE EXPRESSION FOR DEBYE SCREENING To temperature , the thickness of charge cloud let the potential ф on the plane x=0 is held at a value ф0 by perfect transparent gain. To compute→ ф(x) assume that the ion electron mass ratio M/m is infinite So ions do not move but from uniform background of +ve charge. We can say that M/m is large enough that the inertia of the ion prevents them from moving significantly on the time scale of the experiment. Poisson ‘s eqn → Ԑ0∇2Ф= Ԑ0∂2ф/∂x2= -(eni-ne) (z=1) If the density for away is n∞, we have ni= n∞ In present of a potential energy qф, the electron distribution function is F(u)= A exp[-{(mu2/2)+(qф)}/kTe] Te= temperature of electron
- 9. CRITERTION FOR IONIZED GAS TO BE PLASMA It be dense enough that λd << L Single species system or neutralized plasma are not strictly plasma but the mathematical tools of plasma physics can be used to study such system.