Abstract: The paper puts forward the idea about "C1 discrimination" and "thermally induced principal optical axis" for thermal lasing effect in tube lasing medium.The parameter C1 is a factor of the second term of the temperature distribution expression in the cross section of the tube lasing medium.The positive or negative value of C1 indicates the direction of the gradient between the inner wall and outer wall,relatively indicates the operating mode of the laser.In the effect of thermal lensing,basically the temperature gradient determines the distribution of refractive index in the radial direction.So it is called "thermally induced principal optical axis".This paper derives two dimension transfer matrix of ray and the focus length of the thermal lens,meanwhile points out the main method of improving beam quality.