Separately, spare parts have helped Ukraine add about 20 airplanes to its air force, a senior US defense official said Wednesday, although it's not clear where the parts came from.

Grand total: It would add up to $3.4 billion in US assistance to Ukraine since the invasion began, if the second $800 million package is approved.

What happens with all this firepower? It's not entirely clear. An interesting CNN report focused on how the US loses track of the weaponry it sends to Ukraine.

I asked CNN's Oren Liebermann, who helped write both of the stories about American military aid, what to make of all these additional weapons likely headed from the US to Ukraine.

Pay attention to the importance of artillery, he told me. It is expected to be a big part of the next shipment, and it was an important (though far smaller) part of the last $800 million package.

Why wasn't more artillery sent to this point?

LIEBERMANN: Because artillery was not the type of weapon needed to defend Kyiv. In the swamps and forests of northern Ukraine, not to mention the Chernobyl exclusion zone, artillery was not a critical part of the fight. With the focus now in Southeast Ukraine, artillery and other long-range weaponry absolutely is critical.

Is this new technology or a game-changer in the fight?

LIEBERMANN: Let's be clear -- artillery isn't new tech. Maybe the systems are newer and offer a bit more precision or more firepower, but artillery isn't some newfangled piece of military hardware that's never been seen before. Quite the contrary -- it's been an integral part of wars for many, many decades, if not a couple centuries at this point.

And yet it's viewed by the US and its partners/allies as one of the most important pieces of weaponry to get to Ukraine ... and fast. Ukraine can burn through artillery ammo quickly, so it's important to get them a very large supply ASAP.

How does the Pentagon view its responsibility for these weapons once they're in Ukraine?

LIEBERMANN: That's not viewed as critical. It's DoD's job to get it to the border, then Ukraine takes it from there to wherever they believe it's needed. Ukraine has a nearly insatiable appetite right now for more weaponry, and that's what the US is trying to meet, along with the help of other countries.

The US is training about 50 Ukrainians in a country outside of Ukraine (it's not clear which one) on how to use the Howitzer rounds.

"This is to train the trainers; it's a smallish number of Ukrainians, little bit more than 50 -- they will get trained on how to use the Howitzers and then they'll be able to go back into Ukraine and train their colleagues," the official said.

The US has not seen any indication Russia has moved to prepare its nuclear arsenal for use, and Starr and Cohen report that US officials still feel there is only a very remote likelihood Putin would cross that line.

From Starr and Cohen: Highly classified US military plans continue to be updated about what everyone believes is an almost unthinkable scenario: the use of a nuclear weapon. The US military "has planned all this out," a senior defense official said.