# Implications of China’s Nuclear Expansion for Strategic Stability

The looming prospect of the United States facing two peer nuclear adversaries raises serious questions about whether significant changes to U.S. nuclear strategy and forces are necessary, and whether it is possible to maintain strategic stability in such a system. Will China’s dramatic nuclear expansion, including more than 300 new silos for intercontinental-range ballistic missiles require a counter-expansion of U.S. nuclear capabilities, or posturing existing forces differently? Will the dynamics of a three-sided system undermine strategic stability by creating first-strike incentives that drive nuclear escalation in crisis, and by driving a new arms race spiral that would make limits on strategic nuclear arms untenable? Does the longstanding U.S. policy of maintaining nuclear counterforce capabilities for targeting adversary nuclear forces make these challenges unmanageable?

Fortunately, the worst outcomes are avoidable if each peer maintains a high degree of survivability for a sufficient portion of its forces. The United States does not necessarily need to build more nuclear weapons, as some analysts have called for, and can trust that certain long-held tenets of nuclear stability remain applicable to future challenges. It is possible to maintain first-strike stability and avoid qualitatively new arms race dynamics among three major power nuclear adversaries, even if one or more incorporates elements of nuclear counterforce into its strategy.

Furthermore, possession of sufficient survivable force elements reverses the traditional idea that concentrating warheads for silo-based intercontinental ballistic missiles onto a smaller number of multi-warhead missiles drives instability. The same holds for the bipolar case, but in the three-peer problem this becomes more important. In the interest of maintaining strategic stability, the United States should welcome rather than seek to dissuade Chinese and Russian moves to concentrate their silo-based warheads on multiple-warhead missiles.

These are bold claims, and the idea of welcoming multi-warhead missiles in adversary forces borders on heretical. But the basic rationale is as sound as it is tautological, namely, that counterforce strategies can only involve targeting those adversary forces that are targetable. If each side’s targetable portion is sufficiently small, then each can cover the targetable forces of multiple adversaries with a fraction of its own forces.

This leaves the balance for other purposes, including the assured second-strike capability that is at the heart of maintaining strategic stability. And this situation is further improved if targetable adversary forces are concentrated on fewer missiles.

A simple mathematical model analysis shows how this works, and why maintaining “enough” survivability across nuclear forces can avoid any meaningful “use or lose” pressures that might otherwise undermine stability. Testing these claims involves a bit of math, but nothing beyond high-school algebra. Parsing the equations is not necessary to follow the arguments below but can enhance them for those not inclined to skip over, so please bear with me.

**First-Strike Stability in a Multi-Adversary System**

Math can make people go cross-eyed. However, it has a long history of shaping how nuclear planners think about targeting — and measuring the basics of nuclear deterrence.** **First-strike stability among two or more nuclear adversaries means that after a counterforce exchange, in which each side uses segments of its own nuclear forces to target those of its opponent(s), each can still impose “unacceptable damage” that would outweigh any conceivable benefit of initiating the attack. Stating this stability condition mathematically allows analysts to test assumptions and illustrate implications for force planning. For each side, first-strike stability means satisfying the expression *N – N_{CFexc}≥Du*, where

*N*is the initial number of deployed warheads,

*D*

*is the sum total of unacceptable damage for all adversaries, and*

_{U}*N*

*is the number of warheads lost in the counterforce exchange, including any expended and any destroyed on the ground.*

_{CFexch}What constitutes unacceptable damage for leaders in different countries is a matter of great subjectivity. Some believe delivering a single or few warheads is sufficient, while others argue the answer is adversary dependent and could in some circumstances require destruction and damage corresponding to the use of at least hundreds of warheads. Ultimately, this type of deterrence strategy always involves trying to identify some threatened response that will convince an adversary not to attack. It generally assumes that threatening a greater scope or level of damage, if the threat is credible, will be more likely to succeed.

While it is possible to proceed with the analysis without quantifying “unacceptable damage,” there is another fundamental question that analysts cannot easily defer: Why would any rational strategy plan to engage in nuclear counterforce targeting (which focuses nuclear strikes on an opponent’s nuclear forces) if all sides understand that such strikes cannot deny the ability to impose unacceptable damage in return? One explanation developed and reviewed in recent years is that full confidence in survivability will always remain elusive, and therefore counterforce and other forms of nuclear competition are unavoidable. Another explanation is that targeting nuclear forces can itself contribute to imposing unacceptable damage, both directly because adversaries value their nuclear forces and indirectly because strikes on nuclear forces will likely cause damage that extends beyond those targets. Put simply: If adversaries expect that being on the receiving end of nuclear counterforce strikes will also mean the incidental destruction of other things they value, whether military, industrial, or civilian, then threatening such strikes may have significant deterrent value even if they cannot prevent a devastating counter-response.

Weapons allocated for counterforce might then decrease or even eliminate remaining requirements for unacceptable damage. Furthermore, wherever nuclear counterforce can contribute to imposing unacceptable damage, it may be preferable on moral and legal grounds to deliberate targeting of civilian populations and infrastructure.

Accepting that for whatever reason some states will incorporate nuclear counterforce into their strategies, the simplest case involving two adversaries with identical arsenals can show why fielding multiple-warhead missiles is traditionally considered destabilizing. If a country initiates and expends its entire force in a counterforce attack, the attacked side loses a fraction of its forces equal to the average number of warheads that each attacking warhead destroys. I will call this the counterforce efficiency parameter C =*N*_{CFexc /}*N*. For a single target such as a missile silo, it is the number of warheads per target (warhead concentration) divided by the number of attacking warheads required to destroy the target (target hardness). In simple terms: If you cluster multiple warheads on each missile (resulting in a high value of the parameter *c*), you risk losing a greater percentage of deployed warheads in one strike than if those same warheads were dispersed across a larger number of missiles.

From the defender’s perspective, the condition for first-strike stability becomes 1 – C≥*Du/N*. If on average each delivery vehicle carries more warheads than are required to destroy it (*c *> 1), the stability condition cannot be satisfied. A disarming attack is then achievable, and a resulting first-strike incentive makes crises unstable. Even before reaching this limiting value, there is a threshold for counterforce efficiency above which the opponent’s surviving forces are insufficient to impose unacceptable damage. One critically important note is that this instability arises not just because one side risks losing its nuclear weapons if it does not use them first, but because that first use can provide the initiating side with some meaningful strategic benefit, namely, to disarm its opponent and save itself from the threat of destruction.

Major nuclear powers endeavor to avoid this outcome by maintaining a survivable posture for a significant portion of their deployed forces. Submarines at sea and mobile land-based missiles are especially important in this regard because they are difficult to target. Possessors field these force elements to reduce the overall counterforce efficiency their adversaries might achieve. This makes stability possible even if some portion of their force consists of highly concentrated soft targets.

Accounting for survivable force elements within a simplified model that treats such elements as perfectly survivable, the most stressing scenario for the defender is one in which the attacker uses no more warheads than are necessary to destroy the defender’s vulnerable forces. The condition for first-strike stability with survivable force elements is then

(1)

In this expression, *f** _{S}* is the survivable fraction of the force, the sum (indicated by ∑

_{i}) is over all adversaries, and the last term on the left applies if the defender can avoid targeting adversary forces that were used in the initial attack. If counterforce strategy incorporates more than direct targeting of deployed forces, such as command and control or non-deployed weapons, these requirements could enter either as a fixed additive term or by adjusting counterforce efficiency parameters.

To more clearly illustrate first-strike stability among three peers, we can again simplify to the fully symmetric system in which all have the same force size, structure, posture, and strategy. Assuming further than one side expends the vulnerable portion of its arsenal in an initial counterforce attack, expression (1) becomes

(2)

One key result of expressions (1) and (2) is that when targetable portions of adversary forces are concentrated through approaches such as placing multiple warheads on a single missile and/or unhardened (high values of *c*), *it is easier rather than harder to maintain first-strike stability*. This is because targeting the vulnerable portion of adversary forces requires fewer warheads, leaving more available for the assured response role.

States may and have endeavored to hold at risk more survivable elements of adversary forces, but among those with developed arsenals, these efforts focus more on finding hidden forces than overcoming them with greater numbers of counterforce nuclear weapons. If such efforts succeed, they increase nuclear counterforce requirements by an amount that could be large (e.g., if nuclear capabilities are the only reliable means of targeting a large force of dispersed mobile missiles) but could also be small or even wholly insignificant (e.g., if conventional torpedoes can target ballistic missile submarines). To put it simply: Acquiring greater ability to target adversary nuclear forces does not create a need to allocate a bunch of additional nuclear weapons to counterforce if those new targets are concentrated and/or if conventional weapons are well suited to the task.

Figure 1 is a graphical depiction of expression (2). The dashed line denotes the boundary between a region below that is always first-strike unstable because survivable forces are insufficient to impose unacceptable damage, and a region above where first-strike stability is possible even if opponents incorporate comprehensive nuclear counterforce into their strategies. For any opponent that does not incorporate nuclear counterforce, which might remain the case for China despite its ongoing nuclear expansion, the entire region above and including the dashed line is stable.

*Figure 1. First-strike stability in a fully symmetric three-peer system with counterforce targeting. The vertical axis is the fraction of forces that are survivable, and the horizontal axis is the fraction of the total force required to impose unacceptable damage on both adversaries. The counterforce efficiency parameter c indicates how many targetable warheads on average each attacking counterforce warhead can destroy. *

Shaded regions in Figure 1 indicate regions of stability for particular values of the counterforce efficiency parameter *c*. For example, if one-third of a side’s initial deployed force is required to impose unacceptable damage on both adversaries (*D** _{U}*/

*N*= 1/3), and if on average each attacking warhead can destroy two targetable warheads (

*c*= 2), then first-strike stability is attainable if at least 56 percent of each side’s force maintained in a survivable posture (for example, on submarines and mobile missiles). If, on the other hand, all targetable missiles carry single warheads (

*m*= 1) in hardened silos (

*h*= 2), maintaining first-strike stability is more challenging, requiring that nearly 80 percent of forces are survivable.

The United States maintains survivability across a significant fraction of its forces, potentially sufficient to enable first-strike stability with counterforce strategy against two peer adversaries. Notifications under the New START Treaty enable a rough estimate of U.S. force survivability. Neglecting heavy bombers as concentrated soft targets that unless dispersed are targetable with a small number of warheads, the United States deploys approximately 1300 warheads. Treating the 400 U.S. ICBM warheads as targetable and the remainder as survivable sea-based warheads, roughly 70 percent of U.S. forces are survivable.

Russia might have approximately the same fraction of its deployed strategic warheads on more survivable mobile long-range missiles and submarines, based on public estimates of force structure. For China, that fraction may currently be closer to 80 percent, based on public estimates of Chinese force structure. Based on those same estimates, China’s survivable force fraction would fall to a much lower level of roughly 35 percent if it achieves rough numerical parity with the United States and Russia by fielding intercontinental range ballistic missiles in 300 new silos and replacing existing single-warhead missiles across its force with multiple-warhead variants already existing or under development. As shown in Figure 1, maintaining strategic stability with lower levels of survivable force fraction is possible for countries like China that do not emphasize nuclear counterforce in their strategies.

The United States (like Russia and in the future perhaps China) retains the ability to further increase survivability by alerting bombers and launching long-range silo-based missiles under attack. Day-to-day survivability is lower, though, since only a portion of the submarine fleet is at sea at any given time. Assuming roughly half of U.S. submarines are at sea at any given time, day-to-day survivability is less than 40 percent. In the fully symmetric model situation, maintaining first-strike stability in peacetime with comprehensive counterforce targeting might only work if targetable forces are very highly vulnerable and concentrated. Of course, that is precisely the case for submarines in port. Writing off submarines in port as well as off-alert bombers suggests a relatively high day-to-day survivability above 50 percent.

Critics of missiles with multiple warheads (and of land-based intercontinental-range missiles in general) might argue that silo-based long-range missiles are nonetheless the first weapons one would use in a first strike, and are therefore inherently destabilizing. It is true that *in the event of a first strike* a possessor is likely to use such weapons, but that does not mean they make a first strike any more rational and more likely. As long as the existence of assured response capability means that a first strike cannot deliver a strategic benefit to the attacker, multiple-warhead missiles do not actually pose a “use-or-lose” dilemma. If an adversary is prepared to undertake an attack that no rational logic can support, then in the absence of multiple-warhead-carrying long-range missiles analysts should only expect to see some other element of the force used instead.

**Arms Race Stability in a Multi-Adversary System**

In a multi-peer system with comprehensive counterforce targeting, satisfying the condition for first-strike stability is necessary but not necessarily sufficient for maintaining arms race stability or even equilibrium. For an arms race equilibrium to exist, any such state might also require enough warheads postured for potential use in a counterforce strike (which I will call *N** _{FS}*) to cover any combination of adversaries’ targetable forces:

Like first-strike stability, this kind of arms race stability is possible among adversaries that maintain survivability for significant portions of their forces. For a major nuclear power, the number of warheads suitable for a first strike might be at least as large as the sum of deployed intercontinental-range missile warheads and submarine-launched warheads postured under continual at-sea deployment.

In the simplified case of identical arsenals and strategies, the condition for arms race equilibrium becomes:

Just as for first-strike stability, *vulnerability and concentration of targetable forces make it easier rather than more difficult*** **to achieve this type of arms race equilibrium.

In one sense, this equilibrium is unstable because adversary moves to disperse or harden targetable forces, or to expand that segment of the force, increase targeting requirements for an adversary determined to maintain comprehensive counterforce as an element of its strategy. However, incentives for such moves and countermoves are tempered if all can maintain confidence that the survivable segments of their forces provide the capability for assured response.

Figure 2 is a graphical depiction of expression (3). It shows, for example, that if half of the attacker’s deployed force is available for a counterforce strike and each attacking warhead can destroy on average two targetable warheads (*c* = 2), arms race equilibrium is achievable if at least 50 percent of each side’s force is survivable. If, on the other hand, all targetable missiles carry single warheads (*m* = 1) in hardened silos (*h* = 2), nearly 90 percent of the forces must be survivable for the same attacking force to execute a comprehensive counterforce strike against targetable forces.

*Figure 2. Arms race equilibrium in a fully symmetric three-peer system with counterforce targeting. The vertical axis is the fraction of forces that are survivable, and the horizontal axis is the fraction of the total force available for employment in a counterforce strike. *

For nuclear powers like the United States that maintain forces with relatively high survivability fractions and counterforce suitability, it should be possible to avoid an arms race even while retaining counterforce options against two peer adversaries.

**Implications for U.S. Policy**

This analysis suggests three implications for U.S. nuclear policy and planning. First, it is possible to maintain first-strike stability and arms race equilibrium among three major nuclear powers, even if they incorporate counterforce targeting in their strategies. Doing so requires that each maintains a sufficient fraction of its deployed forces in a survivable posture. The United States must continue to ensure a high degree of survivability in its deployed forces, and in future arms control arrangements it should consider measures that favor the more survivable platforms.

Second, while it makes sense to favor survivable platforms over silo-based missiles, to the extent Russia and China will nonetheless field silo-based systems the United States should not attempt to dissuade the fielding of multiple-warhead variants in that element of their nuclear forces. Contrary to traditional interpretations, concentration of targetable warheads enhances rather than degrades strategic stability among major nuclear powers that maintain survivability for significant portions of their nuclear forces. It does so by helping to ensure that even opponents who incorporate counterforce targeting in their strategies will retain an assured second-strike capability.

Third, for any side that incorporates counterforce targeting, maintaining strategic stability does not require matching the combined force of potential adversaries. China’s nuclear expansion does not mean the United States necessarily needs a larger nuclear force. Rather, it must ensure and posture survivable forces sufficient to inflict unacceptable damage on both potential adversaries, even after or as part of a counterforce exchange.

Finally, astute readers will note the dubious (yet in some sense longstanding) strategic logic of insisting on targeting all vulnerable adversary forces while at the same time encouraging those same adversaries to prioritize deployment of more survivable platforms. One way out of this contradiction would be to abandon nuclear arms limitations and pursue a three-sided arms race. The other two options are to abandon any embrace of comprehensive counterforce targeting for major nuclear adversaries or embrace with abandon this curious feature of the bizarro world of nuclear strategy.

*Dr. Aaron Miles is a fellow at the Center for Global Security Research at Lawrence Livermore National Laboratory. He is currently serving on assignment as a senior advisor in the U.S. Department of State Bureau of Arms Control, Verification and Compliance, and served previously in senior nuclear policy positions at the White House Office of Science and Technology Policy and in the Office of the Secretary of Defense. His policy interests include deterrence, arms control, and nonproliferation.*

*The views expressed herein are the author’s alone, and do not necessarily reflect those of any organization or entity.*

Image: Wikipedia