Opening Remarks Why the details? Not everything I said is included in the slides. Please pay attention to the lectures and catch the most essential points. Form your own opinions and thoughts. Should ask questions. Try to attend classes as much as you can.

Let us make a deal. Turn off your cell phone during the class. Do not conduct private conversation. If you have questions, you may directly ask me. If you have urgent need to leave the room, you are excused. Otherwise do not leave the classroom frequently. After several classes we should have a review session. Druing the meeting let us exchange ideas about the teaching.

Let me reiterate: Most of the stuff I discuss during the class may not be found in standard textbooks. The Universiy gives me this teaching task and responsibility. Personally I take it seriously. I sincerely wish that you can learn something new from this course. Let us work ogether and optimize the result.

Graduate Courses Normal and regular courses Designed for basic education and training. Special topic courses Expectations are very different. My responsibility is to introduce some new and special stuff. My duty is to promote kinetic theory and space plasma physics.

About the title of the course “Nonlinear processes in space plasmas” “Space plasma physics and kinetic instabilities”

Planning & Rationale Basic and general theory Theories of plasma instabilities Discussion of several important phenomena in space physics

Introducing Plasma Physics

Space Plasma Physics & Plasma Astrophysics Plasma physics was initially advanced for controlled thermonuclear fusion research. There are special processes that mainly occur in space plasmas. Space plasma physics is a field basically developed for understnading space ans astrophysical plasmas.

The birth of plasma physics Plasma is an ionized gas. Charged particles can be affected by electric and magnetic fields. It was thought that plasma may be studied in a similar way as we dealt with a neutral gas which is generally treated as a fluid. Since a neutral gas may be studied with hydrodynamics, plasma may be considered as a conducting fluid.

As a result, magnetohydrodynamics was born. MHD theory was unsuccessful in fusion experiments in mid 1950s. Kinetic theory began to attract attention. Discovery of numerous new instabilities that pushes the birh of modern plasma physics.

Why ? Scientists gradually realize that the basic physical property of plasmas is critically different from that of a neutral gas.

How ? In a neutral gas inter-particle collisions dominate but in a plasma wave-particle interactions prevail. There exist many instabilities in plasmas while very few instabilities occur in gases. Plasma turbulence can greatly modify the physics of a plasma. As a result, many new physical processes can take place in plasmas that are not possible in gases.

In plasmas there are many wave modes. Instabilities imply that these wave modes can be amplified. The enhanced waves can result in nonlinear processes that can change the fundamental property. Particle-particle interactions are much less important than the interactions of waves with particles. There are many other reasons. Consequently we must recognize plasma physics is a new branch of physics, and in general plasmas should not be treated as a gas.

A Landmark Work A paper by L. D. Landau was published in 1946. In this paper Landau showed that Langmuir wave may be damped while there are no collisions. Later on this paper led to the realization of wave-particle resonance. It also led to the discovery of kinetic instabilities in plasmas.

Why plasma physics is important to space physics and astrophysics? The reason is simple: In stellar and solar atmosphere, in interstellar or interplanetary space plasma is everywhere. How can one understand the physics in these regions without the knowledge of plasma physics?

Three approaches to study plasmas Single particle dynamics MHD and fluid theories Kinetic theory

Why kinetic theory is important? Many physical processes in plasmas depend on microscopic particle motion. However, fluid dynamics considers only averaged particle motion. And single particle dynamics cannot represent an ensemble of particles. Kinetic theory seems to be the best tool available to study plasma physics.

Force Fields Gravitational field Electric and magnetic fields Ambient or background field Fields associated with waves Self-consistent fields

In fluid dynamics theory Density, velocity and pressure are all functions of coordinates space that is dimensional. All physical quantities and the force fields are statistically averaged. As a result, the theory does not and cannot describe microscopic particle motion.

Commonly use terms in kinetic theory Phase space Distribution function Probability density Kinetic equation Fokker-Planck equation Lenard-Balescu equation Vlasov equation

Conclusion Fluid theory may be useful if we only want to study dynamic issues. However, if we want to explain some important phenomena and understand the underlying physics, fluid dynamics theory is not sufficient. Remember: plasma is very different from an ordinary gas.

Density and Fields In real space particles move randomly. Microscopic fields and density fluctuate in time and space. Concept of phase space is important. Only statistical averaged quantities are of interest. Kinetic theory is developed for this goal.

Microscopic Picture In a real plasma fields and particle density are random microscopic quantities. All particles are moving stochastically. However, each particle is governed by the equation of motion which is controlled by microscopic fields are . Each particle moves continuously in phase space.

Intermission

Phase-Space Orbit

Continuity Equation