Deuterium-tritium (D-T) fusion is expected as a next-generation energy source. In this problem, we consider a single reaction model inside a magnetic confinement fusion reactor.
In a vacuum coordinate space, a uniform magnetic field of magnetic flux density B exists in the positive z-direction.
At the coordinate origin (0,0,0), a deuterium nucleus (mass mD, charge +e) and a tritium nucleus (mass mT, charge +e) that were initially at rest undergo a fusion reaction, producing an alpha particle (mass mα, charge +2e) and a neutron (mass mn, charge 0).
In this reaction, the total mass after the reaction is less than before — this mass defect Δm is completely converted into the kinetic energy of the products (alpha particle and neutron) according to Einstein's mass-energy equivalence.
The alpha particle and neutron are emitted in opposite directions in the xy-plane, following conservation of momentum. The alpha particle undergoes uniform circular motion in the xy-plane due to the Lorentz force from the magnetic field. The neutron, having no charge, is unaffected by the magnetic field and travels in a straight line toward the reactor wall.
The speed of light in vacuum is c. The kinetic energy of the reactants before the reaction is negligible compared to the released energy; treat particles as starting completely at rest.
Also, the speeds of the products are sufficiently small compared to c — use non-relativistic (classical) mechanics for kinetic energy and momentum calculations.
Find the radius R of the uniform circular motion of the alpha particle.
Find the radius R of the alpha particle's circular motion in meters (m) and give the answer as a positive integer equal to the value multiplied by 100. (Example: if R=2.53 m, answer 253.)