1. Introduction to Plasma Physics and Plasma-based Acceleration

2. What is plasma? Plasma: ionised gas
Ionised by high temperature, radiation, electrical discharge, …
“Fourth state of matter”
Mixture of free electrons, positive ions, neutral atoms
Behaviour is dominated by electro-magnetic interactions between charged particles

3. Where do we find it? Almost everywhere!
99% of all matter in the universe is in the plasma state!
Sun, stars, giant gaseous planets, interstellar matter…
Fluorescent lamps, plasma screens
Nuclear fusion devices
Plasma-based accelerators

4. Why plasma is important
The sun, a plasma cloud we all know and love (image: NASA)

5. Plasma for nuclear fusion
JET tokamak (Image: ITER)
Nuclear fusion can only happen when matter is hot enough to bring positive nuclei together → plasma

6. Io transits Jupiter
20th December 2000

7. Essence of a gas Short-range Van der Waals interactions
Except for collisions, particles move freely
No significant collective effects

8. Essence of plasma
Long-range EM interactions
Interaction strength does not fall off:
Coulomb force: ~1/r2
Number of particles: ~r2
Total interaction: ~1
Collective effects dominate behaviour; collisions are relatively rare

9. Debye length
Two electrons in a plasma with temperature T and density n, distance of closest approach b0, determined by Coulomb repulsion: Average distance given by: n-1/3

10. Debye length
There should be few binary collisions in a “true” plasma, so b0 << n-1/3: Debye length: Plasma parameter:

11. The “truest” plasma
Nd > 105: interstellar “gas”, solar corona (both low density), thermonuclear plasma in fusion device (very hot) Nd < 100: solar atmosphere discharge (too cold), laser-produced plasma (too dense)

13. Debye shielding
A charge in a plasma is shielded by charged particles (electrons) in the plasma Typical shielding distance: Debye length Number of particles involved in shielding: Plasma parameter

14. Debye shielding
Assume a point charge q in a plasma with density n and temperature T Potential Φ is given by: Boltzmann density for electrons:

15. Debye shielding
Linearise differential equation for eΦ/kT << 1: Solution (Green’s function for Helmholtz equation):

16. Debye shielding
Point charge q is shielded by a cloud of charged particles with radius λd and total charge –q At distances shorter than λd : individual particles “visible” At long distances: collective behaviour only, individual particles “invisible” (true plasma)

17. Consequences
An equilibrium plasma is charge neutral (electrons smooth over any imbalances) A quasi-neutral plasma behaves as an ideal gas:

18. Plasma frequency
Divide electron thermal speed by Debye length to obtain plasma frequency: This is the characteristic frequency of small-amplitude plasma oscillations

19. Plasma oscillations
Electrons are displaced by distance X with respect to ions, charge imbalance provides restoring force: Will be treated in depth later. + - + - + - + - + - +

20. Oscillations versus collisions
In a “true” plasma, we have: Thus, collective effects dominate over collisions, and the plasma can be far from thermal equilibrium

21. Summary A plasma is an ionised gas where
collective interactions dominate over individual interactions
characteristic frequency: ωp
shortest length scale: λd
enough particles in “Debye sphere” to ensure good shielding of charges
quasi-neutral most of the time