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Natural SciencesPhysicsMathematical PhysicsNuclear PhysicsParticle PhysicsAccelerator PhysicsAccelerator ShieldingNonlinear DynamicsNonlinear MechanicsNonlinear Plasma DynamicsNonlinear VibrationAcceleratorsBeam Acceleration SystemsHadron AcceleratorsLongitudinal Beam DynamicsNonlinear Beam AnalysisParticle Acceleration In PlasmasParticle Acceleration Mechanisms