Several scenarios for how Russia might soon use a nuclear weapon seem possible: (1) a detonation over the Black Sea, causing no casualties but demonstrating a resolve to cross the nuclear threshold and signaling that worse may come, (2) a decapitation strike against the Ukrainian leadership, attempting to kill President Volodymyr Zelensky and his advisers in their underground bunkers, (3) a nuclear assault on a Ukrainian military target, perhaps an air base or a supply depot, that is not intended to harm civilians, and (4) the destruction of a Ukrainian city, causing mass civilian casualties and creating terror to precipitate a swift surrender—the same aims that motivated the nuclear attacks on Hiroshima and Nagasaki.

Any response by the Biden administration would be based not only on how Russia uses a nuclear weapon against Ukraine but also, more important, on how Russia’s future behavior might be affected by the American response. Would it encourage Putin to back down—or to double down? Cold War debates about nuclear strategy focused on ways to anticipate and manage the escalation of a conflict. During the early 1960s, Herman Kahn, a prominent strategist at the Rand Corporation and the Hudson Institute, came up with a visual metaphor for the problem: “the escalation ladder.” Kahn was one of the primary inspirations for the character Dr. Strangelove in Stanley Kubrick’s classic 1964 film, and yet the escalation ladder remains a central concept in thinking about how to fight a nuclear war. Kahn’s version of the ladder had 44 steps. At the bottom was an absence of hostilities; at the top was nuclear annihilation. A president might choose to escalate from step No. 26, “Demonstration Attack on Zone of Interior,” to step No. 39, “Slow-Motion Countercity War.” The goal of each new step upward might vary. It might simply be to send a message. Or it could be to coerce, control, or devastate an adversary. You climbed the ladder to reach the bottom again someday.

The “escalation vortex” is a more recent and more complex visualization of a potential conflict between nuclear states. It was developed by Christopher Yeaw, who served as chief scientist at the U.S. Air Force Global Strike Command from 2010 to 2015. In addition to the vertical aspects of the escalation ladder, the vortex incorporates horizontal movement among various domains of modern warfare—space, cyber, conventional, nuclear. An escalation vortex looks like a tornado. An illustration of one, featured in a Global Strike Command slideshow, places the worst outcome at the widest part of the funnel: “the absolute highest levels of permanent societal destruction.”