That's because you can either have ionisation via electron impact and via electromagnetic radiation, strong electrostatic fields (and here I mean really field ionisation not ionisation due to accelerated charges) or thermal ionisation. The first mechanism is by far the most efficient one.

Next comes the radiation (or photon) ionisation, but you need high intensities for that and one ionisation process usually involves multi-photon processes (except for really high energetic photons).

This means that if you have no primary electrons to start with (even microwave or rf plasmas are mainly produced by initially generated electrons that oscillate in the varying field and induce impact ionisations) your ionisation rate will go down with the plasma density.

The very last type is only related to particles in a thermal equilibrium, i.e. with a Boltzmann energy occupation. Here your plasma density as well as your ionisation rate are pure functions of temperature (dependent on the gas species, of course).

Generally I would say this: higher density -> more collisions -> less free path-> less probability for particles to gain enough energy for ionization (take account of the higher threshold energy for ionization than other processes).

In a plasma, the electron impact ionization rate is calculated as the integral of the electron energy distribution function on the cross section. The electron energy distribution function can be calculated solving the Boltzmann equation that is a function of E/N, or the concentrations normalized to N, therefore the distribution is a function of 1/N where N is the total particle density. As a consequence, threat of ionization by electron impact decreases with the electric field. 

However, the mechanism of ionization is not simple and in some cases is not well understood. The mutual interplay between electron impact excitation, ionization, dissociation and processes involving only heavy particles gives a complex behavior. As Johannes pointed out, if you do not have electrons, the ionization process starts with other mechanisms than electron impact ionization and therefore heavy particle ionizative recombination or direct ionization can be relevant.

The ionization energy is some electronvolts per atom, if you heat a high density gas it will loss the energy due radiation because you will have a lot more collisions as said Aleksandar.

Ionization energy for hydrogen is 13.6 eV that corresponds to 160.000ºK. The sun surface temperature is 5800ºK and it heats the earth.

Accordingly Gianpiero Colonna (he wrote at the same time than in my previous post) if it is installed a power supply between two electrodes the voltage difference applied to every atom is the voltage of the power supply divided by the atoms^(1/3) in the volume between both electrodes. So if you have 1000 times more atom density you will have to increase the voltage ten times.

You must take in account also the Pashen curves and breakdown voltage, if you increase the atom density it will happens a breakdown, the voltage will goes to zero and no ionization is possible. You can find an accurate calculation of the breakdown voltages of some gases at following link

At label “Fisica”, equation number 070 “Paschen breakdown voltage of gases”, you have to use the graph at the right of the table.

Data Useful formula and excel tables for plasma physics V04

If you are talking about the density of the plasma then, this may be explained according Saha Equation:

http://socrates.berkeley.edu/~phylabs/adv/ReprintsPDF/HAL%20Reprints/06%20-%20Intro%20to%20Plasma%20Physics_CH1.pdf

The ration (ni/nn) is inversly proportinal to ni!!

Increasing the ion density (ni) will reduce the neutral atoms (nn) that could be ionized. So, by increasing the number of ions, the remained neutrals is less hence the rate of ionizing the rest is low.

This is only in case you are talking about the relation between the ionization rate and the plasma density.

--

If you are asking about the gas density, then I think the best answer is the collision probability.

Imagine the billiard game. If you you are going to strike one ball only, this ball may move long distances if the board is empty then it may move with high velocity and collide the board edges many times. But if the board is "crowded" , as example the first strike with the 15 balls, the energy will be distributed among them all. Some balls may not even move, i.e. they did not acquire a lot of energy.  The energy of the ball (the electron) which strikes the other balls (ions) will be distributed, so many ions may not reach the state of ionization.

@ Mohamed.

In your comment there is a misunderstanding. The Saha equation is an equilibrium equation and therefore gives you the equilibrium distribution independently of the value of the rates.

The billiard example in principle is correct, but it should be taken with some attention, because you are talking about elastic collisions and not to inelastic as ionization. Moreover, the mass difference between electrons and heavy particles makes the elastic collisions not very efficient from the point of view of energy transfer, because  in a collision of this kind (light particle with heavy particle) there is the maximum transfer of momentum to the light particle, but the heavy particle does not change its velocity. This is the reason why in a discharge the electron temperature can be much higher than the temperature of heavy particles and the joule heating is a slow process. In fact recent papers by Popov, Pintassilgo and Guerra show that the fast heating of a plasma column is not due to the Joule heating but to the strong interaction between internal levels, chemical processes and free electrons, which is more efficient than the pure joule mechanism.

To consider all the mechanisms, you should consider the Boltzmann equation, that includes also the contribution of the magnetic field. The two-term approximation is the most simple approach, you can find it in the attached paper. 

For the fast heating, one should solve the Boltzmann equation, together with the chemical and level kinetics. Give a look to the Popov papers. 

As far as I know, there is no general simple equation for describe the whole mechanisms. This aspect is being investigated in these years and it is not well understood yet

@ Gianpiero Colonna

Thank you so much for your comment.

I meant that the same view in general could be used to understand the effect of the density. Also, I differentiated between the plasma density and the gas density in two different point according to what @ Alex meant by his question.

Best regards for all.

=========================

I tried to introduce the Saha equation in an excel table (see attached file) but it seems not working), I will look for Popov, Pintassilgo and Guerra papers accordingly Gianpiero said.

Thank you for your answers so far. I attached some contourplots of the Ionisation degree in plasma where the drop with denstiy is seen and a one contourplot of the ionisationrate out of the K-Shell of a swift Ca^+18 ion (3.5 MeV) in the 1s^2 ground state flying through a plasma of a certain density and temperarture.

Both show the same depndency with increasing density

Do anybody has experimental  ion concentration table or values?

Generally speaking at fixed temperature,ionization will tend to increase with density,through atomic orbitals delocalization,thusdocumenting the well-known pressure ionization effect.

Dear Claude,

The pressure ionization is another effect that is important at very high density. There are two different contributions, the most important is the ionization lowering due to the presence of the plasma, the other one is the change in the number of bound levels in an atom in a plasma (Mott effect). Some details can be found in "Quantum Statistics of non ideal plasmas" by Kremp, Schlanges, Kraeft. The  density should be above 10^20 cm^-3, However this is a thermodynamic aspect, dealing with the equilibrium composition. In weakly ionized plasma, during the discharge, the effect discussed here is different, because at the plasma as the plasma density increase, at constant field, the rate of ionization decreases with the density because the rates are a function of E/N. 

I have added the Saha equation and some others to the excel sheet. It can be found at the sheet "Fisica", equation number 190

Data Useful formula and excel tables for plasma physics V05