# What affects the lifespan of plasma

When I was reading up ion thruster and ionocraft, I saw this concept of plasma lifespan. But I can't find any information or study done on what affect the lifespan of plasma. Is it pressure? Electric field strength? Or something else?

There exists three conditions a plasma must satisfy (taken from [1]) :

1. $\quad \lambda_D \ll L$
2. $\quad N_D \ggg 1$
3. $\quad \omega \cdot \tau \gt 1$

Here $\lambda_D$ denotes the Debye length:

$$\lambda _D \equiv \Bigg ( \cfrac{\epsilon_0kT_e}{ne^2} \Bigg )^{\frac{1}{2}}\, ,$$

and L is the dimension of the system.

The second equation simple states that the density is high, so that the plasma cannot be treated as a simple Newton fluid of neutral charges.

And the third condition is the one you ask:

Here $\omega$ is the typical plasma oscillation frequency and $\tau$ is the mean time between collisions with neutral atoms. If this condition doesn't hold, it behaves like more a neutral gas rather than a plasma.
The plasma frequency is

$$\omega_p = \Bigg ( \cfrac{n_0^2e^2}{\epsilon_0 m} \Bigg )^{\frac{1}{2}}\, ,$$

where $n$ is the electron density, $m$ the mass of an electron and $e$ the electron charge.

When an ion and an electron collides at a relative low velocity (you can take a Maxwell-Boltzmann velocitiy distribution), there exist a probability of recombining into a neutral atom. In case the loss of plasma by recombination is larger than the one of generation, the plasma will for short or long disappear. The loss of plasma can be due to radiative or three-body (a third particle is involved) recombination.
Or for instance if the magnetic bottle isn't strong enough to maintain the plasma. The plasma involves also a pressure which has to be taken into account. Hence when you cannot hold the plasma by an external pressure, the plasma will cool down and increase in volume, and the electrons and ions will recombine --> no longer a plasma.

Therefore the recombination rate (electron and ion) has to be at least equal or less than the generation rate (collisions of atoms lead to an (more) ionized atom and an electron).

BTW: There many good books concerning about Plasma Physics, but I like this the most:

• [1] Introduction to Plasma Physics and Controlled Fusion, 3rd edition, by Franics Chen