system in general, since the charge density and current density induced by many
electrons in plasma alter the electric and magnetic fields.
2.2.1 Maxwell Equations
Let us start with revisiting Maxwell equations.
Most of the students involved in science and/or engineering have learnt the
Maxwell equations. Maxwell’s predecessor Michael Faraday was a genius in the
frontier of electricity and magnetism as an experimentalist at his era. Given his poor
family background, he was restricted to receiving higher education. But his talent
was flowering in the UK Royal Institution where he was a technical official in the
laboratory of Prof. H. Davy. During the 1830s, he was diligent in his responsibilities
conducting experiments on electricity and magnetism and also accustomed to
tabulating daily reports on his experimental results. One of his great achievements
is Faraday’s Law indicating physical quantities of electricity and magnetism are
related to each other.
M. Faraday, however, was not able to express his experimental results by
universal expressions due to lack of education in advanced mathematics. However,
his accumulated results taken over to James C. Maxwell, and he resulted in one of
the most important formulas of physics. Maxwell was educated at the University of
Cambridge and demonstrated his scientific power as a student there. The
experimental verification of his theories has to wait until the demonstration of
electromagnetic waves by H. Hertz.
Maxwell read over Faraday’s experiment note many times and wondered if there
was a unified mathematical relation to explain Faraday’s experimental results. At
that time, there was also a time when fluid dynamics was comprehensive and studied
vigorously. Fluid equation by Euler is expressed by the concept of density field,
velocity field, and other “fields.” Maxwell finally found that coupled partial
differential equations like fluid equations can be derived by introducing concepts
of electric field and magnetic field to electricity and magnetism, respectively. The
concept of similarity (similar transfer) has led him to the great equations. Finally, in
the book called “Theory of Electromagnetism,” he published Maxwell equations that
explain all the experimental results by Faraday in 1865.
Equation (2.2.1) is the induction relation invented by Faraday, and it indicates
that the time variation of magnetic field produces electric field. This relation
becomes important in plasma physics, for example, when we deal with particle
acceleration in magnetic reconnection observed on the solar surface. The change of
topology of magnetic field induces electric field which accelerates charge particles.
The time variation of the electric field will induce the current in plasmas and induced
magnetic field as seen in (1.3.2). Then, this magnetic field will return to (1.3.1), and
the electromagnetic wave is generated to propagate in the plasmas. A typical
collective phenomena in plasma are waves since charged particles in plasma interact
each other over the long-distance coupling with many particles.
40
2 Laser Absorption by Coulomb Collision
electrons in plasma alter the electric and magnetic fields.
2.2.1 Maxwell Equations
Let us start with revisiting Maxwell equations.
Most of the students involved in science and/or engineering have learnt the
Maxwell equations. Maxwell’s predecessor Michael Faraday was a genius in the
frontier of electricity and magnetism as an experimentalist at his era. Given his poor
family background, he was restricted to receiving higher education. But his talent
was flowering in the UK Royal Institution where he was a technical official in the
laboratory of Prof. H. Davy. During the 1830s, he was diligent in his responsibilities
conducting experiments on electricity and magnetism and also accustomed to
tabulating daily reports on his experimental results. One of his great achievements
is Faraday’s Law indicating physical quantities of electricity and magnetism are
related to each other.
M. Faraday, however, was not able to express his experimental results by
universal expressions due to lack of education in advanced mathematics. However,
his accumulated results taken over to James C. Maxwell, and he resulted in one of
the most important formulas of physics. Maxwell was educated at the University of
Cambridge and demonstrated his scientific power as a student there. The
experimental verification of his theories has to wait until the demonstration of
electromagnetic waves by H. Hertz.
Maxwell read over Faraday’s experiment note many times and wondered if there
was a unified mathematical relation to explain Faraday’s experimental results. At
that time, there was also a time when fluid dynamics was comprehensive and studied
vigorously. Fluid equation by Euler is expressed by the concept of density field,
velocity field, and other “fields.” Maxwell finally found that coupled partial
differential equations like fluid equations can be derived by introducing concepts
of electric field and magnetic field to electricity and magnetism, respectively. The
concept of similarity (similar transfer) has led him to the great equations. Finally, in
the book called “Theory of Electromagnetism,” he published Maxwell equations that
explain all the experimental results by Faraday in 1865.
Equation (2.2.1) is the induction relation invented by Faraday, and it indicates
that the time variation of magnetic field produces electric field. This relation
becomes important in plasma physics, for example, when we deal with particle
acceleration in magnetic reconnection observed on the solar surface. The change of
topology of magnetic field induces electric field which accelerates charge particles.
The time variation of the electric field will induce the current in plasmas and induced
magnetic field as seen in (1.3.2). Then, this magnetic field will return to (1.3.1), and
the electromagnetic wave is generated to propagate in the plasmas. A typical
collective phenomena in plasma are waves since charged particles in plasma interact
each other over the long-distance coupling with many particles.
40
2 Laser Absorption by Coulomb Collision