THE NUCLEAR SPEAR: CASABA HOWITZER

eight of 0.87 meters. The volume would therefore be about 0.4 cubic meters. As previously mentioned a Casaba-Howitzer charge would have a yield ranging from sub-kiloton to a few kilotons, so presumably it would be smaller and of lower mass than a pulse unit. THE NUCLEAR SPEAR: CASABA HOWITZER (ed note: In 2018 Matter Beam discovered errors in the original calculation. The figures below have been updated)

The Casaba Howitzer is the result of research into reducing the spread of the particles produced by a nuclear pulse unit. Make the cone narrow enough and it becomes a destructive beam.

The original nuclear shaped charge design called for the use of a tungsten plate. The particles that resulted from the detonation of a pulse unit would fit inside a cone with a spread of 22.5°. The particles would be relatively slow (between 10 and 100km/s depending on thrust requirements) and rather cool (14000°C in transit, 67000°C after hitting the plate).

As noted before, using lighter elements, such as plastics or even hydrogen, in a thick and narrow instead of wide and flat shape, you can achieve a very narrow cone and very high particle velocities. A Science & Global Security report from 1990 used polystyrene as the propellant material to produce a particle beam with a spread of 5.7° and a velocity of 1000km/s.

Particle velocity is derived from the Root Mean Square equation. It can be written as such: 24939 is a constant equal to Boltzmann's constant (1.38*10-23) divided by unitary molar mass in kg (1.66*10-27) times the degrees of freedom of motion (3). Temp is the nuclear detonation's temperature in Kelvin, and Mass is the mass of the propellant used in kg/mol. For an atom bomb (108 K), uranium (238) will be ejected at 102km/s. In a fusion reaction (109 K), deuterium (2) will be ejected at 3530km/s.
 * Particle velocity = (24939 * Temp / Mass) ^ 0.5

The difficulty is in transmitting this thermal energy to the propellant, and keeping the particle cone focused.

In a propulsion pulse unit, it is not known how efficiently a nuclear shaped charge is able to heat the propellant. Most sources cite a 85% of the device's energy being sent in the desired direction. It is unknown also whether this is before or after some of the propellant is accelerated in the wrong direction, and whether larger pulse units are more efficient (higher propellant mass fraction). This is important as it would allow a thermos-dynamic estimation of the particle velocity.

It would be reasonable to use a lower figure when calculating the amount of energy delivered to the propellant. Scott Lowther gave a 50% figure for small fission charges. An SDI nuclear weapons study, Project Prometheus, experimentally tested Casaba Howitzer weapons using plastic propellants. It achieved 10% efficiency. A Princeton University study from 1990 on third-generation nuclear weapons cited 5% instead, but for fusion devices with ten times better beam focus.

Effectiveness
Despite the reduction in cone spread, the stream of particles produced by by Casaba Howitzer dissipates much more quickly than an electro-magnetically accelerated particle beam or a laser.

It is possible to reduce the beam angle to 0.006 degrees in width, as reported by the third-generation nuclear weapons study. 0.057 degrees has been experimentally achieved by project Prometheus. The trade-off is much lower efficiency than propulsive units (5-10% vs 80-85%).

The theoretical maximal performance of a thermonuclear device is 25TJ/kg. Modern weapons are able to achieve 2.5TJ/kg, but this figure is for large weapons that have better scaling. Smaller warheads such as those tested for project Prometheus are likely to be in the kiloton range, and mass about 100kg. Better understanding of fission ignition has reduced the nuclear material requirement down to a kilogram or less.

A nuclear detonation only lasts a microsecond, so we can assume that the entire energy of the unit is delivered to the target in a single pulse of duration 10-6seconds. As the particles produced expand in a cone with an angle θ, we can use the following equation to calculate the destructive potential at various distances: Intensity is measured in watts per square meter. Irradiance is joules per square meter. Yield is how much energy the nuclear charge delivers, converted to joules. Efficiency ranges from the 0.85 of a propulsion unit to the 0.05 of a Casaba Howitzer. θ is the cone angle. Distance is between the nuclear detonation and the target, in meters.
 * Intensity = (Yield * Efficiency * 10^6) / (3.14 * (tan(θ) * Distance) ^2)
 * Irradiance = (Yield * Efficiency) / (3.14 * (tan(θ) * Distance) ^2)

Let us calculate some examples: Small Casaba Howitzer (50kg) 0.01 radian directivity (0.057 degrees) 5kt yield, 10% efficiency: 2.09TJ Distance 1km: Irradiance = 673GJ/m^2 Distance 10km: Irradiance = 6.7GJ/m^2 Distance 100km: Irradiance = 67.2MJ/m^2 Distance 1000km: Irradiance = 672kJ/m^2

Large Casaba Howitzer (1000kg) 0.001 radian directivity (0.0057 degrees) 1Mt yield, 5% efficiency: 209TJ Distance 1km: Irradiance = 6728TJ/m^2 Distance 10km: Irradiance = 67.3GJ/m^2 Distance 100km: Irradiance = 672MJ/m^2 Distance 1000km: Irradiance = 6.7MJ/m^2

Futuristic Megaton Nuclear lance 0.0001 radian directivity (0.00057 degrees) 1Mt yield, 20% efficiency:836TJ Distance 1000km: Irradiance = 2691GJ/m^2 Distance 100000 km: Irradiance = 269MJ/m^2To determine destructive capability, we can model the Casaba Howitzer as a direct energy weapon. We can recreate the particle strike as a laser weapon firing a single pulse with equal properties.

We will describe the strike as a laser pulse of duration 1 microsecond, containing X energy and with Y spot radius. A 1.63 micrometer laser focused by a 2cm diameter mirror consistently produces the same spot sizes as a 0.01 radian beam. A 20cm mirror is used for 0.001 radian beams, and 200cm for 0.0001. We test penetration against Aluminium. Small Casaba Howitzer: X = 2.09TJ 1km, Y = 0.994m: 734mm penetration 10km, Y = 9.94m: 0.73mm penetration

Large Casaba Howitzer: X = 209TJ 50km, Y = 4.97m: 586mm penetration 500km, Y = 49.7m: 0.59mm penetration

Futuristic Megaton Nuclear lance: X = 836TJ1000km, Y = 9.94m: 293mm penetration 5000km, Y = 49.7m: 2.35mm penetration The results reveal that the Casaba Howitzer is an extremely destructive weapon, with the larger models able to strike at distances usually reserved for lasers. Even a small Casaba Howitzer is effective at up to several kilometers, using technology tested in the 80s. Larger, more modern devices can strike at extreme distances. Futuristic devices will reach particle velocities of about 10000km/s, so time to target is negligible.

However, these distances are lower than those of powerful lasers, so the Casaba Howitzer will need a delivery system such as missile, or be used in defensive roles.

Making use of the Casaba Howitzer
The Casaba Howitzer's advantages are numerous, and can be exploited in four ways: A MIRV'S warheads Hard science fiction with a military focus usually boil down to where the author has placed their marker on the sliding scale between missile and laser dominance. Make lasers too powerful, and they make mass missile attacks uneconomical. Make missiles cheap and fast enough, and you can overwhelm any laser defense.
 * Terminal warhead

Missiles are hindered by the requirement to track the target and follow until impact. Lasers are increasingly effective as missiles close the distance to their target. Past a certain point, any missile touched by a laser is quickly destroyed. So quickly, that a laser defense's primary limitation is the time it takes to switch targets. In other words, a laser defense sets up a 'death zone' around itself, within which any wave of missiles will quickly be annihilated.

A combination of efficient lasers, multiple turrets and competent target handling can cut through hundreds of missiles. The counter to this, on the missile side, is to perform randomized high-acceleration maneuvers called 'jinks'. This tactic is already used today by sea-skimming missiles once they enter the range of CIWS defenses. The problem is, in space this requires the missile to have powerful thrusters, lots of propellant and active, autonomous sensors that survive to the terminal stage of its attack. This means that missiles will end up being heavy, hard to bring up to speed, large (easy to track and hit) and expensive due to on-board electronics. These are all characteristics you want to avoid when trying to make massive waves of missiles economical, or if jinking through the death zone. Using a Casaba Howitzer warhead solves this conundrum.

It allows missiles to deal damage from outside the death zone. It also removes the requirement of saving propellant for the terminal stage, or even the necessity of accelerating up to a high velocity intercept. It allows missiles to be lighter and smaller. Depending on the price of the nuclear technology, a few Casaba-Howitzer missiles may be cheaper than multitudes of kinetic impactors. The usefulness of a nuclear shaped charge extends further than just being a warhead. As calculated in the Effectiveness section of this post, the particle cones spread quickly, but remain effective at short ranges.
 * Point defense

In a defensive role, a Casaba Howitzer will have to be lightweight and efficient in its use of fissile material. This is because it must be deployed in numbers comparable to the incoming projectiles. Optimizing for efficiency has the consequence of producing a wide cone. This cone can be used to sweep away missiles in the terminal phase. Close enough, it will outright vaporize kinetics. Further away, it can still damage sensors and shatter propellant tanks through impulse shock. The large angle of the cone is advantageous, as it would reduce prevision requirements against jinking missiles, and might even catch several missiles at once.

Other advantages of using Casaba Howitzers as a point defense is that it can easily be aimed, does not consume power and has infinite firing rate. If you detect missiles coming in, dump your entire payload of defensive drones and have them point at targets. Once they come within range, all can detonate simultaneously.

This might actually be the preferred tactic, to prevent previous nuclear detonations from interfering with the detonation of subsequent charges. This is a concern if the Casaba Howitzers use fusion fuels that are sensitive to external sources of neutron radiation. Example defensive Casaba Howitzer: 100kg, 10kt yield 85% efficiency: 35.56TJ beam Beam velocity 1000km/s Beam angle: 10 degrees Effective range (penetrates 5mm of aluminium): 16km This warhead can destroy anything within a 6.15km2 circle up to 16km away. It reaches targets in less than 16 milliseconds, and unlike a pin-point laser, it affects the entire surface of the target at once. The awesome power of a nuclear shaped charge does not have to be used directly to damage targets. It can be used in innovative ways. Instead of being used to generate high velocity particles in a narrow cone, a Casaba Howitzer can be used as a nuclear version of modern shaped charges. A metal cone is put in the way of a nuclear-heated beryllium filler. It is accelerated by the blast, like in an Explosively Formed Projectile. The only requirement is that the energy deposited into the metal lining is not sufficient to vaporize it.
 * Booster

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