Plasma  science  and  technology  Basic  concepts

ATHENS 2015Instituto Superior Técnico

Instituto de Plasmas e Fusão Nuclear

Vasco Guerra

Since the dawn of Mankind men has tried to understand plasma

physics...

As  perguntas  fundamentais

•What is plasma?

•How is plasma created?

•Why is plasma interesting?

•What is plasma good for?

Plasmas:  o  inícioThe basic questions

As  perguntas  fundamentaisComo  se  forma  um  plasma?How is plasma created?

As  perguntas  fundamentaisQuatro  estados  da  matéria...  e  não  quatro  elementos!Four states... or four elements???

As  perguntas  fundamentaisO  que  é  um  plasma?

•Ionized gas

•Quasi-neutral

•Exhibits collective behavior

The potential energy of a typical particle is much smaller than its kinetic energy

What is plasma?

As  perguntas  fundamentaisThe origin of the word “plasma”

•The word was introduced in 1928 by Irving Langmuir

Langmuir, “Oscillations in ionized gases,” Proc. Nat. Acad. Sci. U.S. (1928) 14 628

From the Greek πλάσμα (to mould), since the brightness of Crookes’ discharge tubes “moulds” to the shape of the tube

Analogy with blood plasma

•“. . . we have observed some phenomena of remarkable beauty which may prove to be of theoretical interest.”

Langmuir, Science (1924) 60 p 392

As  perguntas  fundamentais

For nearly everything!

Para  que  serve  um  plasma?What is plasma good for?

As  perguntas  fundamentaisWhat is plasma good for?

•Light electrons, tend to have high “temperatures,” while the ions, heavier, tend to have low “temperatures” (non equilibrium!)

•Reactions that normally can occur only at high temperatures can take place at low temperatures!

•Plasma emits UV and visible radiation

Plasmas are useful for nearly everything!

As  perguntas  fundamentaisFundamentals

•Debye shielding

•Plasma frequency

•Plasma parameter

•Ionization degree

As  perguntas  fundamentaisDebye shielding

•Test charge: positive ion, infinite mass

•Attracts the electrons and repels the other positive ions

•The electron density in the vicinity increases

•A negative charge cloud forms - shielding - which tends to cancel the test charge

⇥(r) =1

4�⇤0

QT

r

As  perguntas  fundamentaisDebye shielding

•Electrostatic potential

⇤(r) =1

4⇥⌅0

QT

rexp

�� r

�D

⇥•Debye potential

�D =�

⇥0kT

n0e2

⇥1/2

As  perguntas  fundamentaisDebye shielding

Quasi-neutrality does not hold inside a Debye sphere

As  perguntas  fundamentaisDebye shielding

• The phenomenon is known as Debye shielding and is the first exemple of a plasma collective behavior

The hypothesis of the typical particle’s potential energy being much smaller than its kinetic energy is used in the linearization of Poisson’s equation

As  perguntas  fundamentaisDebye shielding

• Debye’s potential due to a charge in a plasma decays much faster than in vacuum

•For r≫λD the shielding cancels qT and φ(r)≃0

•qT does not have to be a special particle: each charged particle in the plasma tends to establish its own shielding cloud

➡Plasma condition: λD ≪ L (typical dimension of the system) ≡ “quasi-neutral”

As  perguntas  fundamentaisDebye shielding

Some typical values

As  perguntas  fundamentaisPlasma parameter

•Distance between particles ~ n�1/30

•Potencial energy due to the closest neighbor ~

•Typical kinetic energy ~12m�v2⇥ =

32kTe

Plasma: number of electrons in a Debye cube >>1

� = n0�3D � 1➡ Plasma condition:

⇠ 1

4⇡"0

e2

r⇠ 1

"0n1/30 e2

As  perguntas  fundamentaisIonization degree

Plasma can coexist with another state

• In the ionosphere there are regions where 99% of the gas is neutral and only 1% is ionized

• We have then a partially ionized plasma

• The plasma parameter Λ is calculated only with the ionized component (and we have Λ>>1 and λD ≪ L)

• Usually there is a continuous exchange of charge between the particles of the neutral gas and the ones of the ionized plasm

• Medium is characterized by the ionization degree, ne/(ne+n0)

As  perguntas  fundamentaisPlasma frequency

E

Oscillatory motion of angular frequency ωpe=

As  perguntas  fundamentaisPlasma frequency

•It is one more example of collective behavior

•We can define a “ionic plasma frequency” and a total plasma frequency,

ωp2=ωpi2+ωpe2

•To have a plasma, the collective behavior must dominate over the individual collisions

➡Plasma condition: ωpe ≫ νc (electron-neutral collision frequency), or ωpeτ ≫ 1

As  perguntas  fundamentaisHow to study plasmas?

•Single particle motion

•Kinetic equations

•Fluid equations

As  perguntas  fundamentaisThe wonderful world of plasmas!

As  perguntas  fundamentaisVoyager I

http://www.jpl.nasa.gov/interstellarvoyager/