Context :

Aims : Using the recently observed torsional Alfvén waves in solar prominences , we determine the ionisation state of the plasma by taking into account that Alfvén waves propagate in a partially ionised prominence plasma .
We derive the evolutionary equation of waves and compare the analytical solutions to observations to determine the number density of neutrals .

Methods : Using a single fluid plasma approximation , where the wave damping is provided by the Cowling resistivity , we study the temporal evolution of waves .
By comparing the solution of equations with observational data ( period , amplitude , propagation speed ) , we determined the value of the Cowling resistivity that led us to draw a conclusion on the amount of neutrals in the partially ionised plasma , a quantity that can not be measured directly or indirectly .

Results : Our results show that damped torsional Alfvén waves are an ideal diagnostic tool for the ionisation state of the plasma .
Using a simple model , we find that at the observational temperature of torsional Alfvén waves , the number of neutrals , is of the order of 5 \times 10 ^ { 10 } cm ^ { -3 } .

Conclusions :