What causes the spirals to be inward in the bubble chamber images? 
My understanding is that the circular paths are caused by the action of the Lorentz force on the electrons and positrons. 
However, I'm not sure why the circular paths are going inward. I have two ideas in mind. The first is that this could be caused by drag forces from the atmosphere of the bubble chamber. The second possibility is that this is caused by Bremsstrahlung radiation.
Which of the two factors plays a more significant role? Is there any calculation/evidence/reference to support one answer over the other? 
Edit: Changed "cloud chamber" to "bubble chamber."
 A: In a cloud chamber (or any other detector) the particles are moving through a material medium, so they steadily lose energy (that can also suddenly lose energy which results in a kink in the track).
Less energy means lower speed which means less momentum $p$, and the radius of curvature $R$ goes by
$$ R = \frac{p}{qB} \;, $$
where $q$ is the particles charge and $B$ the strength of the magnetic field.
So, as energy is lost, the curve gets tighter and tighter.
A: Low energy electrons lose energy to ionization of the medium they’re traversing. The ionization comes from the charged particle interacting electrically with atomic electrons as it moves through atoms. 
This is a good thing: that ionization is what the chamber is detecting and displaying. 
A: As can be seen in the label of the picture you show, it is a bubble chamber picture. The label says : 
" A bubble chamber works on the same principle as a cloud chamber except that spiral tracks are seen as well."  
Cloud and bubble chambers make charge particle tracks visible by their scattering off atoms of the medium, ionizing them and creating the little accumulation of "bubbles"  which  reflects the light so a photograph is taken. The little dots are visible and can be photographed. Cloud chambers are not used in magnetic fields so spirals are not seen.
This scattering generates energy loss as a particle traverses the medium and this loss is seen in the reduction of the radius as shown in the answer by dmckee .
There is also the radiation loss of a charged particle turning in a circle , called synchrotron radiation, which for the picture shown is in the Xray region, i.e. not enough energy to give the drastic reduction in radius seen in the picture. The effect of radiation loss to the ionization curve is shown in the link, in page 4.
There are ionization curves of particles through matter, and are used in analysing bubble chamber pictures, because they depend on the momentum and mass of the particle, and allow to identify the low momentum  tracks in the bubble chamber experiments, but that is another story.
A: Let us compare this phenomenon with this in a particle accelerator, a undulator or a free-electron laser.  
The difference to a cloud chamber is the high vacuum inside these devices. All other “ingredients” are the same: charged particles, moving straight forwards and an external magnetic field.
Even without the collision with other particles the charges radiate, and in the same time get deflected (change their direction) and loose kinetic energy. So the answers which claim that the collisions are the only reason for the spiral path, have been given somewhat hastily.
