Spaceship propulsion

The Spaceship propulsion refers to means of moving a spaceship.

Overview
There are numerous types and technologies for propulsion, here, are only those in common use in this universe. Only active and onboard propulsion are considered here, not assisted or provided from an outside source. Antimatter annihilation presents the highest energy density known in existence, which is 180 MJ/μg ; 90 MJ/μg. In fact, antiproton-proton annihilation can provide an Isp = 107 sec. The particular concepts of interest here are Antimatter Catalyzed Microfission/fusion (ACMF), Antimatter Initiated Microfusion (AIM) and cylindrical ambiplasma , which are hybrids of nuclear fusion and antimatter technologies.

Matter-antimatter hydro-plasma drive
There are many types of matter-antimatter (MA) drives or classically called photon drives. The MA drive used here is a water fusion inducing MA reaction drive. This drive has a few advantages over other MA drives.


 * 1) It is still a photon drive just not a pure photon drive and is less efficient in terms of propellant mass spend. The photon name reference comes from the early days of physics, and from the electron e- and positron e+ annihilation. Each act of annihilation releases two γ-photons in opposite directions which impart momentum to the ship for movement, hence, the name reference. As a photon drive it is capable of accelerating the ship to high relativistic velocities. However, like the ion drives its drawback is low thrust, hence, slow acceleration because the photons are near massless. And exhaust mass directly correlates with the amount of power. This low thrust makes photon thrusters unsuited for launching spacecraft into orbit, but effective for in-space propulsion.
 * 2) It is also a plasma drive. As a plasma drive it produces high-thrust suitable for fast reaction and maneuvers. And the plasma can be fine tuned by magnet fields for higher or lower acceleration thrust as well as vectored thrust only limited by the size and design of the nozzle.
 * 3) The water itself serves to contain or conduct heat for extra power generation and also shields the ship from the radiation.
 * 4) The design is relatively simple, easy to maintain and repair. It's essentially a huge chamber full of water and is not so much more complex than a fusion tokamak reactor.
 * 5) Scaling this thruster design is easier than other magnetic field reliant designs. As the size grows so has the size of the magnetic field. However, the magnetic field has to project the same required force but now at a larger distance. This ultimately means the magnet has to grow in size and power to meet the requirement. In the case of the water chamber, the pressure inside the water body as well as the pressure exerted on the outside is the same everywhere. And even though the increase in mass would lead to an increase in water pressure the force applied only needs to be located on the surface. Therefore, the magnets are not required to grow as large as in other designs, hence, are much lighter and consume far less power. Besides they are only really necessary at openings or valves.

Through the insertion of antimatter (AM) and the mixing with water matter (M) a plasma called ambiplasma is formed. The classification of ambiplasma is further divided into heavy ambiplasma (protons-antiprotons) and light ambiplasma (electrons-positrons). In this case both types are being used in the chamber. The power generation / annihilation zone is limited to a cylinder within the chamber. The rate of annihilation per time unit and per unit length is:

$$R_a = ν_a n π R^2 = β_r c N/l_ann = r_0^2 c N^2 / R^2, (β_r < 0.6)$$

$$R_a = β_r c N/l_ann = r_0^2 β_r c B_rel N^2/R^2, (β_r > 0.6)$$

where $$r_0^2$$ is the radius of electron or proton, correspondingly, and R is the radius of the ambiplasma.

In the case of e- e+ annihilation, the rate of emission of γ-photons per second and per unit of length $$N_ph = 2R_a$$.

In the case of p- p+ annihilation (pp&#773;), the rate of emission of charged pions per second and per unit of length is $$3R_a$$.

The maximum rate per square area, per unit time and per unit length is:

As can be seen the power generation is proportional to area size of the nozzle and length of the thruster engine. The most efficient and compact design would be cyclinder within the boundary of a cube.

For the photon part to produce 1 MN an efflux power of 1014 W and the rate of annihilation events $$N'_a \sim 5 × 10^{26} s^-1$$ is required.

For the pp&#773; plasma part to produce 1 MN a mass consumption rate $$dM/d_τ \approx 4.5 × 10^{-3} kg s^{-1}$$, where $$τ$$ is the proper time in the rocket frame. It corresponds to total annihilation power of 2.3 × 1014 W and efflux kinetic power of 5 × 1013 W. The rate of pions production is $$N_π \sim 5 × 10^{24} s^{-1}$$, the rate of annihilation events $$N'_a = N_π/3 \approx 1.4 × 10^{24} s^{-1}$$.

This means the photon thrust part is 0.0028 of the pp&#773; plasma's given equal mix from neutral antihydrogen, hence, total thrust is 1.0028 × pp&#773; plasma.

As the thruster is not meant to be a reactor a complete energy conversion of everything is undesired. After all only part of the water is meant for immediate use as propellant while the rest remains for reaction-, temperature- and radiation-control. Therefore, it is necessary to determine the best fraction for use. Although, everything could be used for maximum thrust, however, that would cool down the core and becomes less efficient as it progresses. Though, this could be considered in emergency situations, the window of effective uses is very narrow and cannot be employed again anytime soon.

Low energy pp&#773;’s annihilate mostly at the surface of nuclei, and thus local energy deposition follows a A2/3 dependence on atomic weight. In effect, the CERN data is compatible with the expression :

$$&isin; \sim 6.4 A^{2/3} [MeV]$$ (3)

Hence, for pp&#773; annihilation in H2, DT or Li2DT, &nu; is always about 3 and &isin; is approximately equal to 0, 12 or 22 MeV respectively. In a H − H&#773; plasma, the electron and the proton populations deplete at the same rate, with a time constant of 5 ns for ρ = 0.07 g/cm3.

AIM: cylinder R~13 mm × L 25 mm; confinement is a spheric cloud of R=8 mm × L 20 mm of 42 ng DHe3; 1011 p&#773; injected as 5 x 108 p&#773; droplets resulting in 0.75 MW for fission with 5 x 1013 W/cm3 or 33 MW for aneutronic fusion. 33MW = 55.2N with 9.22 × 10-5 kg/s and 5.98 × 105 m/s

μ = 2.5 is average molar mass of fuel D + T.

The four principal reaction combinations DT, DHe3 and DD. DHe3 reactions have the advantage that they produce fewer neutrons than DT. DD also produce only ~1/4 neutrons of DT reactions, but DD reactions are around ten times harder to ignite. It is worthwhile nothing that for other reactions using a 3 g mass the number of moles will be 0.6 moles (DHe3) and 1.5 moles (DD). We calculate the number of nuclei in the pellet which is the molar amount multiplied by a constant known as the Avogadro’s number NA.

N(nuclei) = N(moles) × NA = 0.6 moles × 6.022 × 1023atoms/mole = 3.6132 × 1023atoms

We can do a similar calculation for DHe3 and we find that the total energy release in the form of He4 products with energy of 3.67 MeV per reaction is 1.3260444 x 1024 MeV or the equivalent of 51 tons TNT. DHe3 reaction products He4+p exhaust velocity 26500 m/s (8.88% c) and if divided by go = 10 m/s2 gives the specific impulse to be 2.65 million seconds. The maximum enthalpy performance for a fusion based engine, where ho ≈ V2e / 2. This computes to 348 million MJ/kg;