Bending light with temperature gradients

[Samson4]

A quick question about this type of apparatus. The apparatus itself is composed of 2 concentric hollow cylinders. The cylinder at center is cooled below -50C. The atmosphere around the outer cylinder is at room temperature. This creates a temperature gradient in the space between the cylinders. The index of refraction increases as distance from the center cylinder decreases.

Question: If a laser is pointed into a perfectly transparent spot on the outer cylinder, could the laser beam be refracted to orbit the inner cylinder given the space is large enough for such a small change in refractive index

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[Vanadium 50]

I suspect that by the time you have refracted the beam enough to get a circle, you've attenuated the beam into irrelevance.