Exact solutions to the governing dynamic equations of plasma armature electromagnetic railguns

Technical Report · Sat Aug 01 04:00:00 EDT 1987

OSTI ID:6083904

Shahinpoor, M; Hawke, R S

General governing nonlinear differential equations pertaining to the dynamic behavior of a plasma armature electromagnetic railgun are first derived. Three different cases are then considered and the corresponding governing equations are then solved exactly by means of a set of nonlinear transformations. These cases correspond to (1) no-ablation, (2) continuous-ablation, and (3) partial-ablation for which an ablation threshold velocity nu/sub t/ plays a fundamental role. Corresponding to each case, a nonlinear transformation is employed to reduce the nonlinear differential equations to their equivalent linear ones and subsequently allow solution of the pertinent linear differential equations, which are second order, by means of the transition matrix technique. It is concluded that in order to achieve very high projectile velocities the projectile should be injected into the railgun at velocities higher than the ablation threshold velocity. Thus, the ablation may be completely alleviated and the ensuing turbulent drag may be significantly diminished. It is shown that under these conditions one may typically accelerate projectiles up to 30 km/s or more while without hypervelocity injection, for the same railgun and typical operating conditions, one might severely limit the maximum projectile velocity.

• Research Organization: New Mexico Univ., Albuquerque (USA). Dept. of Mechanical Engineering; Lawrence Livermore National Lab., CA (USA); Sandia National Labs., Albuquerque, NM (USA)
• DOE Contract Number: AC04-76DP00789
• OSTI ID: 6083904
• Report Number(s): SAND-87-0473; ON: DE87014442
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420200* -- Engineering-- Facilities
Equipment
& Techniques
99 GENERAL AND MISCELLANEOUS
990220 -- Computers
Computerized Models
& Computer Programs-- (1987-1989)
ABLATION
ACCELERATORS
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL MODELS
NUMERICAL SOLUTION
PERFORMANCE
PROJECTILES
RAILGUN ACCELERATORS
VELOCITY