The Garwin Archive

ABSTRACT Hundreds or thousands of ICBMs armed with nuclear warheads could destroy the United States; even a few could kill millions of people. Blocking or deterring the acquisition or use of such capabilities is highly desirable. This talk, however, deals with the technical problems and prospects for effective defense against ICBMs-- in boost phase, mid-course, and during and after reentry. Topics include detection, tracking, guidance, and the ability to destroy the target or render it harmless. For interceptor missiles: multi-stage propulsion, sensors, and guidance. For directed-energy weapons: generation, propagation, and kill. The revolution in microelectronics and computing, and the experience of decades render some of these problems trivial (in principle), but effective countermeasures vitiate many approaches. Three durable countermeasures against non-nuclear intercept include release of submunitions on ascent, large enclosing balloons, and anti-simulation.

INTRODUCTION.

The guided ballistic missile was first used in warfare September 8, 1944-- the German V-2, bombarding English cities from the continent. The predecessor to the V-2 was the V-1, an early cruise missile with a pulse-jet engine (the "buzz bomb") that British defense forces became quite effective in intercepting. Toward the end of the V-1 campaign, British fighter aircraft would fly next to the buzz bomb and with the wing tip of the fighter would tip the wing of the buzz bomb in order to divert it into less populous areas. It was fortunate that the V-1 did not have a simple contact sensor to cause it to explode when touched in flight. There was no defense against the V-2, except to attempt to destroy it before launch; an effort out of all proportion to the damage caused by the V-2 was expended to this end.

On a flat, non-rotating Earth, without an atmosphere, a ballistic missile attains maximum range for a given launch speed with an elevation angle of 45 deg, and the range increases as the square of the initial velocity, as is evident from high school physics, R = V^2/g; for R in km, V in km/s, g is 0.0098 km/s^2

For missiles of intercontinental range, the fact that the Earth is almost spherical is important, since an initial velocity of 8 km/s that would correspond to a range of 6530 km on a flat Earth now corresponds to infinite range, since it is the velocity required to enter low-Earth orbit (LEO). Using conservation of momentum in the frame of the accelerating rocket (with velocity V(t) and mass M(t)) leads to the rocket equation

dV/dM = -V_e/M --> dV/V_e = -dM/M --> \Delta V/V_e = -\Delta ln M --> M_o/M_f = e^{\Delta V/V_e} (Eq. 1)

where M_o and M_f are the initial and final masses, and \Delta V is the "velocity gain" of the rocket. If Eq. 1 is used in the approximation of continuous staging, the Ve that appears in the formula is reduced from the actual Ve to compensate for the fact that staging is discrete and for the structure discarded at each stage. The limiting speed of a single-stage rocket is simply the rocket nozzle exhaust speed V_e times ln (M_o/M_f). For a rocket with no payload, the ratio M_f/M_o is the "structure factor". In the rocket literature, propellants are characterized by their "specific impulse"-- Isp, measured in seconds, which is simply V_e/g.

It should be observed that even though the mass that can be propelled by a rocket to a given high velocity is exponentially smaller as this velocity increases, according to Table 1 the efficiency of conversion of the thermal energy of the rocket fuel to kinetic energy of the payload remains high-- to velocities well beyond those of interest in ballistic missiles.

The first row is the final velocity V_f; the second \alpha. is the ratio of final velocity to rocket exhaust velocity V_e. The third row is the mass ratio m from the rocket equation, while the fourth row is the energy efficiency in converting to kinetic energy of payload the internal energy of a mass of propellant equal to the initial mass of the rocket less the final payload. Eq. 2 shows the relevant formula,

\epsilon == (K.E.)/(P.E.) = (1/2 M_fV_f^2)/(1/2 V_e^2 (M_o-M _f)) (Eq. 2)

       +----------------------------------------------------------+
       | TABLE 1:  For  final  velocity  Vf  achieved  by  rocket |
       | propulsion   with   exhaust  velocity  V_e = 3 km/s, the |
       | payload fraction is \mu and the fraction of fuel  total  |
       | energy   present   in  the  payload  kinetic  energy  is |
       | &epsilon..                                               |
       +----------------------------------------------------------+
       |                                                          |
       |V_f    3       6       9       12      15      18 km/s    |
       |                                                          |
       |\a1pha 1       2       3       4       5       6          |
       |                                                          |
       |\m     37%     13.5%   5.0%    1.83%   0.67%   0.248%     |
       |                                                          |
       |\eps   59%     62%     47%     30%     17%     9.1%       |
       |                                                          |
       +----------------------------------------------------------+

with numerical values tabulated in the fourth row of the Table.

Table 1 assumes practical "staging", without which there is a firm limit on the speed that can be achieved, even with zero payload.

A "Scud" is a ubiquitous single-stage liquid-fueled missile manufactured in the Soviet Union or indigenously in many nations of the world. Hundreds of Scuds were exchanged between Iraq and Iran, and scores of "extended-range Scuds" armed with high explosive were launched by Iraq against Israel and Saudi Arabia. Iraq had lengthened the fuel tank of the Scud and thus increased its range in producing the al-Husayn missile.

THEATER MISSILE DEFENSE IN ACTUAL WARFARE. (1) On January 18, 1991, a U.S. Patriot air defense system launched its interceptors against an al-Husayn attacking an air base in Saudi Arabia, but it soon became evident that the al-Husayn warhead was not an easy target. The modifications to the Scud had affected the stability of reentry (which normally takes place in these missiles with the warhead still attached to the spent missile), so that the warhead broke off and descended in a tight helix, greatly reducing the effectiveness of the intercept. The missiles usually broke up into three pieces-- the warhead, the fuel tanks, and the

rocket motor, but the Patriot radar and computer were usually able to distinguish the warhead from the other potential targets.

The Patriot system uses a ground-based phased-array radar that continually scans in a flexible fashion a sector of the sky for approaching objects. It characterizes them and, either automatically or via manual intervention, launches one or two interceptors against the aircraft or missile. The interceptor itself is tracked by the radar and steering commands are automatically generated and transmitted in order to intercept the warhead within the atmosphere. The Patriot interceptor is endo-atmospheric, since it relies on aerodynamic forces to maneuver. The interceptor itself carries a receiver of the signal transmitted by the radar, so that in the vicinity of the offensive warhead the interceptor picks up the reflected radar return and relays it to the radar; "track via missile" approach greatly improves the performance of the interceptor against the targets for which it was designed. At the optimum time, high explosive in the interceptor warhead is detonated by the fuzing system, spraying the incoming warhead with steel pellets.

It is entirely reasonable to have a defense against warheads armed with high explosive, just as it is worthwhile to defend against aircraft delivering such weapons.(2)

U.S. defense against theater ballistic missiles is being improved with the substitution of the Patriot Advanced Capability-3 (PAC-3). This is a smaller interceptor that employs "hit-to-kill" technology and is to destroy the incoming warhead by the kinetic energy of its collision rather than by explosively driven fragments. A similar Navy system with endo-atmospheric capability is under development, with the first units being operational in late year 2000 and 2002 respectively.

Enlargement of the area defended from a single interceptor site can be achieved with intercepts outside the atmosphere, and an Army theater high-altitude air-defense (THAAD) system and corresponding Navy theater-wide system are to be available in 2008 and 2010 respectively. Of course, radars

must be able to detect and to discriminate the threatening warheads at greater range for these systems to be effective.(3) And they must also perform technically against targets that may have features that reduce the effectiveness of the defense-- i.e., countermeasures.

DEFENSE AGAINST ICBMS.

A typical intercontinental ballistic missile (ICBM) will have a range of 8000-10,000 km and a speed of around 7 km/s. Minimum propulsion for a given range is achieved with a reentry angle closer to 22 deg than to 45 deg because the range is not small compared with the radius of the Earth. Of course, the atmosphere of depth 10 tons per square meter exerts a substantial drag on the ballistic missile as it rises, so that a practical design does not achieve intercontinental speed within the dense atmosphere; this is accomplished by limiting the thrust and hence the acceleration of the missile. This also limits the "dynamic pressure" and the skin heating on ascent. But too low an acceleration implies excessive "gravity loss", since it is only the excess of vertical component of thrust over the force of gravity that actually results in acceleration of the missile. Even so, a typical large liquid-fueled missile may have a thrust of 1.3 times its gross weight, so that initially only 0.3/1.3 of the thrust accelerates the missile just after liftoff.

The kinetic energy of the RV, which is a good fraction of the total energy of the propellant of the entire ICBM, must be dissipated on reentry. ICBM warheads must be protected by a reentry vehicle (RV) against the heat and deceleration of the atmosphere. A typical peak deceleration is on the order of 60 g. However, only a small fraction of this energy need be absorbed by the material of the RV-- the rest being carried off by the wake of the reentry. Although initial ICBM RVs used a heat-sink approach, this was soon superseded by a much lighter protection system that uses ablative material that gradually sacrifices its heated surface layer and erodes in a controlled fashion on reentry. The RV shape approximates a sharp cone with a small nose radius.

An ICBM of concern to the United States is usually protected in a silo or concealed inside a mountain. It might need to be removed via horizontal tunnel and erected before launch, or it might be stored vertically, and launched in that position after opening a protective door. The missile can

be ignited in the silo, or it can be ejected more gently and ignited as it emerges. The first-stage booster, when fuel is exhausted, is then separated by explosive bolts, as are eventually the second stage and the third stage, so that the warhead travels on its own to the reentry point. In order not to prejudice accuracy because of the uncertain orientation of the warhead on reentry, the warhead can be fitted with monopropellant rocket jets to force it to pitch over to assume the appropriate orientation for reentering along its longitudinal axis. It is then often "spun-up" by additional jets, in order to maintain that orientation for the remaining 20 minutes or so of flight. Alternatively, the alignment with velocity might be delayed until the beginning of reentry, and the RV spun up at that time.

The United States and other countries with multiple warheads or "penetration aids" often use a "bus" (more formally a PBV, for Post-Boost deployment Vehicle) which carries the guidance unit for the missile and which has the job of accelerating each of the warheads (or decoys or penetration aids) sequentially to the proper velocity so that it will fall to its particular target. Bussing may take five to ten minutes in order to distribute the warheads and appropriate decoys to accompany them.

A ballistic missile defense system could interfere with the ICBM either before launch, or in boost phase (during the operation of the first, second, or third-stage engines) during the bus activity, or it could counter a warhead either above the atmosphere or on reentry, until it achieved its detonation altitude. The ICBM presents different vulnerabilities and opportunities for intercept in its various stages:

PRE-BOOST-PHASE INTERCEPT. The United States tries to learn where all potentially threatening missiles are based. It could destroy them preemptively in the case of hostilities. However, some ICBMs are mobile, and if they are out of garrison and not otherwise observed, they are not vulnerable to such attack. Even if the location of the mobile launcher were known at the time of launch of ICBM, if it were in motion it would be safe from destruction by the nuclear warhead on a ballistic missile. But if the mobile launcher could be tracked continuously, then updates could be sent to a maneuvering warhead; the amount of divert fuel required against a moving ground target is negligible since the /Delta V is rigorously(4) less than twice the maximum velocity of the ground vehicle.

BOOST-PHASE INTERCEPT. The United States maintains in high-Earth orbit a set of Defense Support Program satellites (DSP) which for decades have reported in real time every ballistic missile launch of significant size. It was revealed officially that the U.S. observed in this fashion every Scud launched during the Gulf War. With a 6000-element linear infrared sensor that rotates once every ten seconds, DSP can determine the launch point with an accuracy on the order of a kilometer. Since a typical ICBM burns for about 250s, multiple observations are possible and pretty good trajectory information can be obtained in this way.

In the early seconds of boost, an ICBM is vulnerable to a command-detonated mine adjacent to the site or to a rocket-propelled grenade. Even short-burning Scuds could be destroyed by small homing interceptors launched by radio from as much as 50 km distance from the launch site. Normal ICBMs would be vulnerable in boost phase to ground-based interceptors (GBI) (or sea-based interceptors) from anywhere within a region of about 1000 km of the launch site. Such an interceptor would be launched by command on the basis of DSP data, without there ever having been a radar detection of the ICBM. Fitted with a sensor capable of detecting the missile flame, it could direct its limited field of view in the direction commanded according to the data from DSP, and accelerate toward a predicted intercept point. The prediction would need continued refinement, by observation from the interceptor of the current position of the ICBM booster.

But the interceptor would have to be launched from a site sufficiently close and have sufficiently high performance in order to reach the missile while it was still burning. Furthermore, the interceptor could not simply home on the flame but in the late stages of intercept would need to look "ahead" of the flame, in order to strike the solid missile and not sail harmlessly through the tenuous flame. This could be done either by blind reckoning because of the known shape of the flame, or by actual detection of the solid missile with a proper design of the interceptor seeker.

Because of the ocean area east and north of North Korea, North Korean ICBMs aimed at the United States are an ideal target for ground- or sea-based boost-phase intercept. Specifically, it should be possible to use an interceptor of the same gross launch weight as the GBI of the NMD program (about 14 tons, with 12.5 tons of solid fuel) to boost the kill vehicle (of perhaps 60 kg mass and containing some 15 kg of liquid fuel) to a speed similar to that of the ICBM-- 7 km/s, but with larger engines relative to the mass, so it will reach its final speed more rapidly. A simple calculation shows that the sea-based interceptor could be deployed as much as 2100 km downrange from the launch site and still be able to catch the ICBM while it is still burning. We assume a burn time of 250 s to ICBM speed of 7 km/s (an acceleration of three times that of gravity-- "3 g") while the interceptor acquires 7 km/s in 100 seconds--an average acceleration of 7 g. Because the interceptor must rise vertically in the lower atmosphere, it probably moves only about 250 km toward its target while it is burning, and then in the remaining (250-100) seconds moves some 1050 km. So in the burn time of the ICBM, the interceptor can reach out a total of 1300 km from its launch site. The ICBM at an average speed of 7/2 = 3.5 km/s in 250 s moves no more than 875 km from its launch site. The interceptor could be deployed 1100 km east or west of the ICBM trajectory, about 800-1000 km downrange. So there is plenty of room for U.S. navy ships to carry these interceptors. The ships need have no missile-tracking radars.

Such a sea-based boost-phase intercept system is not compliant with the 1972 ABM Treaty; but Russia and the three other parties to the Treaty might well agree to a specific exception, especially if this were combined with progress on lower missile levels in Russia and the United States. My own judgment is that the ABM treaty plays a valuable role in U.S. national security and in the reduction of Russian nuclear weapons, and that it should not be abandoned lightly. Alternatively, Russia and the U.S. might each deploy 15 test interceptors at a new joint ABM test range south of Vladivostok.

The Air Force is developing an airborne laser (ABL) for boost-phase intercept. It is a chemical oxygen-iodine laser mounted in a Boeing 747 aircraft that has the task of focussing through the turbulent atmosphere (further disturbed by the passage of the laser beam itself) in order to weaken or melt the structure on a missile during boost phase. The ABL laser operates at 1.317 \mu m, perhaps(5) at a power level of 3 MW. The ABL will operate at an altitude of 13 km-- most of the time above the clouds and, assuming that the laser works as planned and that laser beam propagation is as assumed, Forden assesses the range for "decisive engagement" from 320 km for the al-Husayn to 185 km for the North Korean Nodong 1300-km-range missile. This assumes that a substantial arc of the missile skin must be softened so that the missile collapses. For a less catastrophic criterion, Forden estimates the range limit from the missile launch point to be 320 km, and 1000 km or more for an ICBM (assuming the ABL downrange from the ICBM launch and so can attack at closer range). He notes that

ABL could be stationed west, south, and east of North Korea for use against Nodong missiles and ICBMs.

BUSSING. This phase has no particular vulnerabilities and will not be further discussed. If one catches the bus toward the end of its maneuvers, one can counter in this way only a fraction of the RVs. Catching it at the beginning seems less likely than doing the boost-phase intercept.

MID-COURSE AND EXO-ATMOSPHERIC INTERCEPT. RVs falling through space are on a highly predictable trajectory, so that repeated radar observation, for instance, can refine that trajectory and contribute to the intercept capability. Intercept of a single RV is simpler with a nuclear-armed interceptor, with an effective kill range measured in kilometers. Several long-range weapons effects can be important in this regard(6) -- x-ray-induced blowoff of the external surface drives a shock into the material of the RV and can damage the warhead by "spall" or by deformation of the structure; the fissionable material can be melted by neutrons from the interceptor thermonuclear warhead.

Large and powerful radars are required to see a reentry vehicle at ranges of several thousand km, and such have long been deployed in the ballistic missile early warning system (BMEWS) in Alaska, Canada, Greenland, and Britain. The criterion is simply that the radar direct enough energy on the RV within the required search time for the reflected energy to the radar to exceed thermal noise. This is embodied in the radar equation:

E_s = E_o \sigma/R^2 d\Omega, (Eq. 3)

where the solid angle d\Omega = \lambda^2/A into which the radar energy is emitted is related to the antenna area A and the wavelength \lambda, on the assumption that the antenna is diffraction limited. The energy Es scattered by the target is proportional to the effective back-scatter cross section &sigma.. The energy received from the radar antenna

E_r = E_s A/4\pi R^2 = E_o A^2 \sigma/(4\pi R^4 \lambda^2)=NkT (Eq. 4)

where R is the range to the target, kT the thermal energy, and N the margin required for losses and to make thermal excursions above the signal threshold sufficiently rare.

Radar and detection theory are highly evolved and can take into account the fact that reentry vehicles do not suddenly appear in space.

The RVs have an easy ride through the vacuum of space, and an ICBM launch for which the RVs do not wish to be seen or identified can provide a vast amount of clutter or chaff