Opening Remarks

1
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.

2
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.

3
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.

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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.

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About the title of the course

• Nonlinear processes in space plasmas
• Space plasma physics and kinetic instabilities

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Planning Rationale

• Basic and general theory
• Theories of plasma instabilities
• Discussion of several important phenomena in
  space physics

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Introducing Plasma Physics

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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.

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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.

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• 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.

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Why ?

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

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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.

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• 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.

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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.

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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?

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Three approaches to study plasmas

• Single particle dynamics
• MHD and fluid theories
• Kinetic theory

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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.

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Force Fields

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

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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.

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Commonly use terms in kinetic theory

• Phase space
• Distribution function
• Probability density
• Kinetic equation
• Fokker-Planck equation
• Lenard-Balescu equation
• Vlasov equation

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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.

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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.

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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.

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Intermission
25
Phase-Space Orbit
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Continuity Equation