1 eV
½ ¼ 1:16 Â 10
4 K
½
ð1:2:1Þ
1eV ¼ 1:6 Â 10
À19 Joule
½
1 eV is the energy that an electron obtains by the electric field with a potential
difference of 1 volt. Note that most of molecule dissociates around T ~ 0.1 eV, since
the molecular binding energy is of the order of 0.1 eV. The fraction of dissociated
and slightly ionized air is a function of temperature in the atmosphere. When the air
is heated to T ¼ 0.2 eV, oxygen and nitrogen are still molecule at T ¼ 0.6 eV, most
of oxygen is dissociated to neutral atom at T ¼ 1 eV, most of nitrogen dissociates
and ionization starts, and at T ¼ 1.5 eV both are fully ionized.
The ionization of condensed matter is also a function of density. Since the fraction
of electron n(ε) with energy ε has the following general form in thermodynamic
equilibrium condition:
n ε
ð Þ / g ε
ð Þf ε
ð Þ,
ð1:2:2Þ
where g(ε) is the density of state and f(ε) is Fermi-Dirac distribution and a function of
T such as exp(ε/Τ). The increase of free electron at high temperature is due to the
latter contribution, while the density effect is due to the former term. Consider two
extreme situations. In low-density limit like the interstellar media in space, density is
about one particle per cm
3 , for example. In low-density case, there are many states
for free electrons escaped from bound state, and g(ε) is large for free state, while
small number for bound state.
Consider a hydrogen atom. It is reasonable to assume the principal quantum
number n* as the maximum bound state, since the orbit radius rapidly increases with
the principal number n from the core and the electron with n > n* is easily
de-trapped. Then, the total number of the bound state is 2(n* + 1)
2 . Even if the
temperature is nearly zero, the probability of free electron is much larger than the
bound electron at low density. This is the reason why space is assumed to be filled by
plasma, although T ~ 0.
1.2.2 High-Density Plasmas
The second extreme condition is the case of very high density. It is well-known that
hydrogen becomes metal at high pressure limit even at T ¼ 0. For the giant planet
Jupiter, it has been assumed that the core region is of metallic hydrogen, and strong
current is generated by rotation to keep strong magnetic field on the surface. This is a
metallic hydrogen problem which is still an open question in experiment as studied
in Volume 2.
It is predicted that any material changes to metal by strong shock compression
like the shock wave for laser fusion at relatively low temperature. Such a phase
transition is called plasma phase transition in condense matter physics. Metallic
10
1 Introduction
½ ¼ 1:16 Â 10
4 K
½
ð1:2:1Þ
1eV ¼ 1:6 Â 10
À19 Joule
½
1 eV is the energy that an electron obtains by the electric field with a potential
difference of 1 volt. Note that most of molecule dissociates around T ~ 0.1 eV, since
the molecular binding energy is of the order of 0.1 eV. The fraction of dissociated
and slightly ionized air is a function of temperature in the atmosphere. When the air
is heated to T ¼ 0.2 eV, oxygen and nitrogen are still molecule at T ¼ 0.6 eV, most
of oxygen is dissociated to neutral atom at T ¼ 1 eV, most of nitrogen dissociates
and ionization starts, and at T ¼ 1.5 eV both are fully ionized.
The ionization of condensed matter is also a function of density. Since the fraction
of electron n(ε) with energy ε has the following general form in thermodynamic
equilibrium condition:
n ε
ð Þ / g ε
ð Þf ε
ð Þ,
ð1:2:2Þ
where g(ε) is the density of state and f(ε) is Fermi-Dirac distribution and a function of
T such as exp(ε/Τ). The increase of free electron at high temperature is due to the
latter contribution, while the density effect is due to the former term. Consider two
extreme situations. In low-density limit like the interstellar media in space, density is
about one particle per cm
3 , for example. In low-density case, there are many states
for free electrons escaped from bound state, and g(ε) is large for free state, while
small number for bound state.
Consider a hydrogen atom. It is reasonable to assume the principal quantum
number n* as the maximum bound state, since the orbit radius rapidly increases with
the principal number n from the core and the electron with n > n* is easily
de-trapped. Then, the total number of the bound state is 2(n* + 1)
2 . Even if the
temperature is nearly zero, the probability of free electron is much larger than the
bound electron at low density. This is the reason why space is assumed to be filled by
plasma, although T ~ 0.
1.2.2 High-Density Plasmas
The second extreme condition is the case of very high density. It is well-known that
hydrogen becomes metal at high pressure limit even at T ¼ 0. For the giant planet
Jupiter, it has been assumed that the core region is of metallic hydrogen, and strong
current is generated by rotation to keep strong magnetic field on the surface. This is a
metallic hydrogen problem which is still an open question in experiment as studied
in Volume 2.
It is predicted that any material changes to metal by strong shock compression
like the shock wave for laser fusion at relatively low temperature. Such a phase
transition is called plasma phase transition in condense matter physics. Metallic
10
1 Introduction