The author created a relativistic physics-based model for examining arbitrarily shaped closed-path beam guide structures.  The Relativistic Momentum Transfer Model simulates force, mass, energy, and velocity.  The model also predicts magnetic, electric, and radiation fields and emissions.  A specific implementation of the design architecture depicted in Fig 4 was created and analyzed using RMTM and is presented in Table 2.  The z-axis roll-out angle is the initial angle of the beam guide in the accelerator region with respect to the x-y plane.

[Table: Table 2  RMTM Simulation of An Example Design.]

| Beam Guide |  | Simulation Output |  |  |  |
| --- | --- | --- | --- | --- | --- |
| Beam Diameter | 5 mm | Minimum Velocity | 99.0 %c | Thrust (z-axis) |  |
| Ion Type | Alpha (He++) | ϒ Calculated using Table 1 | 7.0888 | Accelerator | -2.103 x 10-8 N |
| Ion Pressure | 10-11 atm | Maximum Velocity | 99.05 %c | Top Bend | +42.37 N |
| Total Round Trip Length | 576.9 m | ϒ Calculated using Table 1 | 7.2648 | Decelerator | -2.345 x 10-8 N |
| Total Volume | 11,328 cm 3 | Average Velocity | 99.024 %c | Bottom Bend | -41.34 N |
| Outer Core Radius |  | Ion Cycle Time | 1,943 ns | Total Thrust | 1.03 N |
| Minimum | 6.5 m | Total Number of Ions in Beam Guide | 3.029 x 1012 |  | 0.231 lbf |
| Maximum | 6.527 m | Ion Lifetime | 10 hours | Total Torque | 1.226 x 10-5 N·m |
| Inner Core Radius |  | Ion Mass Expended Each Year | 1.776 x 10-11 kg | Power |  |
| Minimum | 6.25 m | Maximum Magnetic Field | 7.18 T | Accelerator Power | 165 MW |
| Maximum | 6.278 m | Average Magnetic Field | 6.97 T | Decelerator Power* | -165 MW |
| Z-axis Roll-Out Angle | 70o | Average X-Ray Emissions | 5.02 x 10-11 W | * Decelerator generates power |  |

| Samples in Simulation | 2,451,600 | RMTM Version: 2.41 |  |  |  | which was applied to smooth the beam guide structure and avoid discontinuities.

Fig 5 was produced by RMTM and shows the system level force and velocity changes resulting from all ions traveling through a complete circuit of the beam guide.  Fig 5(a) shows the z-axis force and Fig 5(b) shows the resulting system velocity change, assuming an arbitrary system mass of 10,000 kg.  The time scale used on the bottom axes of Fig 5 indicates the position of ions in the engine.  Ions start at the bottom of the engine (time equals zero) and travel through the outer core.  Ions transition to the inner core at 971.5 ns.  Ions complete a round trip when they return to their original starting position at 1,943 ns.  This scale is also used in Fig 6. The vertical axes show the force or velocity change for each segment in the simulation.

[Figure: Fig. 5  Effect of all Ions Completing a Single Cycle in the Beam Guide.]

Each ion starts at the bottom of the engine and then travels up towards the accelerator region in the outer core, imparting a negative force to the system.  The ion’s z-axis velocity is almost constant inside the accelerator, so only a very small force is transferred to the system.  The ion then moves towards the top of the engine and applies a positive force to the system as its z-axis velocity is reversed.  The ion’s z-axis velocity is almost constant inside the decelerator, so only a very small force is transferred to the system.  The ion then returns to the bottom after exiting the decelerator, which applies a negative force.  The velocity change for an ion traveling through a single cycle is small, however the beam guide contains over 3×1012 ions that complete over a half million round trip cycles each second.