to "dry" mass ()(with payload) fraction (), the velocity change () and specific impulse () no longer holds due to the mass losses occurring in antimatter annihilation. Another general problem with high powered propulsion is excess heat or waste heat, and as with antimatter-matter annihilation also includes extreme radiation. A proton-antiproton annihilation propulsion system transforms 39% of the propellant mass into an intense high-energy flux of gamma radiation. The gamma rays and the high-energy charged pions will cause heating and radiation damage if they are not shielded against. Unlike neutrons, they will not cause the exposed material to become radioactive by transmutation of the nuclei. The components needing shielding are the crew, the electronics, the cryogenic tankage, and the magnetic coils for magnetically assisted rockets. Two types of shielding are needed: radiation protection and thermal protection (different from Heat shield or thermal insulation). Finally, relativistic considerations have to be taken into account. As the by products of annihilation move at relativistic velocities the rest mass changes according to relativistic mass-energy. For example, the total mass-energy content of the neutral pion is converted into gammas, not just its rest mass. It is necessary to use a relativistic rocket equation that takes into account the relativistic effects of both the vehicle and propellant exhaust (charged pions) moving near the speed of light. These two modifications to the two rocket equations result in a mass ratio () for a given () and () that is much higher for a relativistic antimatter rocket than for either a classical or relativistic "conventional" rocket. Modified relativistic rocket equation The loss of mass specific to antimatter annihilation requires a modification of the relativistic rocket equation given as where is the speed of light, and is the specific impulse (i.e. =0.69). The derivative form of the equation is where is the non-relativistic (rest) mass of the rocket ship, and is the fraction of the original (on board) propellant mass (non-relativistic) remaining after annihilation (i.e., =0.22 for the charged pions). is difficult to integrate analytically. If it is assumed that , such that then the resulting equation is can be integrated and the integral evaluated for and , and initial and final velocities ( and ). The resulting relativistic rocket equation with loss of propellant is Other general issues The cosmic background hard radiation will ionize the rocket's hull over time and poses a health threat. Also, gas plasma