Typical ‘tactical’ nuclear weapons have a yield of between 1kt and 30kt. They are much smaller than megaton-range thermonuclear strategic nuclear warheads.
Tactical nuclear weapons would be catastrophic for troops or civilians in the Kilometer or two around the blast radius.
Radioactive fallout would depend on burst-height, and would contaminate Russian territory too.
In short, not only does tactical nuclear use carry huge escalation implications and political dangers for Putin; it would be militarily ineffective unless done on a large scale
Russia only has nuclear weapons left as a credible deterrent/threat to wield against the West. If it used nuclear weapons against Ukraine and they did not produce decisive effect, it would badly damage the credibility of the last strategically credible card they hold.
Even if they start conducting tests, it is unlikely to deter Ukraine and NATO would likely double down with support. "Nuclear" is a fear word for most people, however, they are not a significant as most people think.
For comparison, hiroshima/nagasaki was 15kt. A midrange tactical nuke. Using a few wouldn't really change the war or have any significant affect on the balance of forces. The fallout for tactical nukes hasn't been modeled much, and the prevailing winds and weather in the area is erratic and unreliable for profiling if using nukes could affect your own forces. They would have to use numerous which would escalate the situation to a level that would only lead to their destruction which Russia doesn't want. Additionally they would likely alienate china whom they are financially dependent on.
Just the reasoning why I say they won't use them.
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