Consider a plasma consisting of negatively charged electrons and positively charged ions. This plasma is generated using a pulsed laser with duration $t_{pl}$. The plasma will then cool and the ions will recombine. However, in theory, you should be able to pull the electrons and the positive ions apart before they are able to recombine using a strong enough electric field. I tried modeling this with a parallel plate capacitor set-up but my experimental results don't match my calculation. My guess is that I haven't correctly estimated the lifetime of an individual positive/negative pair. Does anyone know of a way to calculate this time scale?

  • $\begingroup$ Since you aren't showing either your experimental setup nor your calculations it's completely impossible to tell which is "wrong". $\endgroup$
    – CuriousOne
    Aug 2, 2016 at 19:19
  • $\begingroup$ CuriousOne is on to something. It is possible that something else is happening. It would probably be helpful to everyone if we knew the laser wavelength, plasma density, laser pulse duration, and peak laser intensity. Are you trying to use the electric field directly to pull them apart or the pondermotive force? Do you expect them to come apart in a single optical cycle of the laser pulse or many? $\endgroup$ Aug 2, 2016 at 19:34

1 Answer 1


There is a way to estimate this rate. The easiest is probably the electron-ion-radiative recombination rate where and electron and ion produce a neutral and a photon. This is for electron temperatures below $400\text{eV}$.

$$ \alpha_r = 5.2\times 10^{-14} \sqrt{\frac{E_\infty}{T_e}} \left[ 0.43 + \frac{1}{2} \ln (E_\infty /T_e) + 0.469 (E_\infty/T_e)^{-1/3} \right] \text{cm}^3/\text{sec} $$

where $E_\infty$ is the ionization energy (of the first electron), $T_e$ is the electron temperature, $\alpha_r$ is the recombination rate. Multiply $\alpha_r$ by the number density to get the frequency of recombination. Take the inverse of that to get the timescale of recombination.

Note that this does not account for three-body recombination which goes like this

$$ \alpha_3 = 8.75\times10^{-27} T_e^{-4.5} \text{cm}^6/\text{sec} $$

where the total recombination rate is $\alpha = \alpha_r + n_e \alpha_3$ where $n_e$ is the electron number density.

See wikipedia for the ionization energies. Note that the CRC values are the ones in electron volts (eV).

The NRL Plasma Formulary is great for things like this. A quick google search will lead you to a pdf of it.

  • $\begingroup$ While this should answer your question it may not address your largely problem at hand. You system parameters might help people in writing answers. $\endgroup$ Aug 2, 2016 at 19:49

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