Lectures in Plasma Physics
By
Dr Mahdya A.Yeser
1.1 Nature of Plasma
As the temperature of a material is raised, its state changes
from solid to liquid and then to gas. If the temperature is
elevated further, an appreciable number of the gas atoms are
ionized and a high temperature gaseous state is achieved, in
which the charge numbers of ions and electrons are almost
the same and charge neutrality is satisfied on a macroscopic
scale. When the temperature of a gas is T(K), the average
velocity of the thermal motion of a particle with mass m, that
is, thermal velocity vT is given by
where κ is the Boltzmann constant κ = 1.380 658(12) ×
10−23 J/K and κT denotes the thermal energy.
Therefore the unit of κT is the joule (J) in MKSA units. In
many fields of physics, the electron volt (eV) is
frequently used as the unit of energy. This is the energy
required to move an e lectron, charge e = 1.602 177
33(49)×10^−19 coulomb, against a potential difference of 1
volt:
1 eV = 1.602 177 33(49) × 10^−19 J .
The temperature corresponding to a thermal energy of 1
eV is 1.16 × 10^4 K (= e/κ). The ionization energy of the
hydrogen atom is 13.6 eV. Even if the thermal energy
(average energy) of hydrogen gas is 1 eV, that is T ∼ 104
K, there exists a small number of electrons with energy
higher than 13.6 eV,
which ionize the gas to a hydrogen plasma.
We can defined the plasma as:
Plasmas are found in nature in various forms (see Fig. 1.1).
Fig. 1.1.Various plasma domains in the n–κT diagram
One example is the Earth’s ionosphere at altitudes of 70–
500 km, with density n ∼ 10^12 m^−3
and κT ≈ 0.2 eV. Another is the solar wind, a plasma flow
originating from the sun, with n ∼ 10^6–10^7 m^−3 and
κT ≈ 10 eV. The sun’s corona extending around our star has
density ∼ 10^14 m^−3 and electron temperature ∼ 100 eV,
although these values are position-dependent. The white
dwarf, the final state
of stellar evolution, has an electron density of 10^35–
10^36 m−3.Various plasma
domains in the diagram of electron density n(m−3) and
electron temperature
κT (eV) are shown in Fig. 1.1.
Active research in plasma physics has been motivated by
the aim to create and confine hot plasmas in fusion
research. In space physics and astrophysics, plasmas play
important roles in studies of pulsars radiating
microwaves or solar X-ray sources. Another plasma
physics is the study of the Earth’s environment in space
Practical applications of plasma physics are MHD (magneto
hydrodynamic) energy conversion for electric power
generation and ion rocket engines
for spacecraft. Plasma processes for the manufacture of
integrated circuits have attracted much attention
recently
1.3Charge Neutrality and Landau Damping
One fundamental property of plasmas is charge neutrality. Plasmas
shield electric potentials applied to the plasma. When a probe is
inserted into a plasma and a positive (negative) potential is applied,
the probe attracts (repels) electrons and the plasma tends to shield
the electric disturbance. Let us estimate the shielding length.
Assume that heavy ions have uniform density (ni = n0) and that there
is a small perturbation in the electron density ne and potential φ. Since the
electrons are in the Boltzmann distribution with electron temperature Te,
the electron density ne becomes
………….(1.3)
where φ is the electrostatic potential and
is assumed.The
equation for the electrostatic potential comes from Maxwell’s
equations :
E = −∇φ
then
we can take the last eq. at
where
Definition of plasma: The forth state of matter
,a quasineutral gas of charged and neutral
particles which exhibits collective behavior.
The plasma conditions :
123-
Ch (2) Plasma Characteristics
2.1 Velocity Space Distribution Function
vx
vy
dvz
dvy
vz
dvx
How
3.3 Equation of Motion of a Charged Particle
4 Velocity Space Distribution Function
and Boltzmann’s Equation
4.1 Phase Space and Distribution Function
4.2 Boltzmann’s Equation and Vlasov’s
Equation