Coulomb Barrier for FusionIn order to accomplish nuclear fusion, the particles involved must first overcome the electric repulsion to get close enough for the attractive nuclear strong force to take over to fuse the particles. This requires extremely high temperatures, if temperature alone is considered in the process. In the case of the proton cycle in stars, this barrier is penetrated by tunneling, allowing the process to proceed at lower temperatures than that which would be required at pressures attainable in the laboratory. Considering the barrier to be the electric potential energy of two point charges (e.g., protons), the energy required to reach a separation r is given by
Given the radius r at which the nuclear attractive force becomes dominant, the temperature necessary to raise the average thermal energy to that point can be calculated.

Index Fusion concepts  

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Calculation of Coulomb Barrier
Of course for headon collisions between particles only half of that energy would be required of each particle, so you could cut that temperature in half. The above temperature is calculated as a reference value.

Index Fusion concepts References: Krane, Sec 14.2  

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Critical Ignition Temperature for FusionThe fusion temperature obtained by setting the average thermal energy equal to the coulomb barrier gives too high a temperature because fusion can be initiated by those particles which are out on the highenergy tail of the Maxwellian distribution of particle energies. The critical ignition temperature is lowered further by the fact that some particles which have energies below the coulomb barrier can tunnel through the barrier. The presumed height of the coulomb barrier is based upon the distance at which the nuclear strong force could overcome the coulomb repulsion. The required temperature may be overestimated if the classical radii of the nuclei are used for this distance, since the range of the strong interaction is significantly greater than a classical proton radius. When trying to model the probability of nuclear fusion, the typical approach is to model it as a "crosssection" for the reaction to occur. This approach is perhaps more apparent in evaluating particle scattering like Rutherford scattering, but the language is often used for nuclear fusion as well. For the purposes here, crosssection can be taken to mean the probability for nuclear fusion to occur. Modeling this crosssection involves taking into account the probability for tunneling through the coulomb barrier. This probability is higher for higher energy particles, but because of the Maxwellian distribution, there are fewer of these high energy particles. Also, the effective energy of collision between the particles for fusion depends on their relative velocities, so the model calculation for nuclear fusion yield involves averaging over all relative velocities. The results of such modeling are presented as a plot of fusion crosssection as a function of average particle energy.
The TFTR reached a temperature of 5.1 x 10^{8} K, well above the critical ignition temperature for DT fusion. References:

Index Fusion concepts References: Krane, Sec 14.2  

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Temperatures for FusionThe temperatures required to overcome the coulomb barrier for fusion to occur are so high as to require extraordinary means for their achievement. Such thermally initiated reactions are commonly called thermonuclear fusion. With particle energies in the range of 110keV, the temperatures are in the range 10^{7}10^{8}K. In the sun, the protonproton cycle of fusion is presumed to proceed at a much lower temperature because of the extremely high density and high population of particles.
References: 
Index Fusion concepts References: Krane, Sec 14.2  

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