EXETER, N.H. — A giant American flag hanging on the wall of a warehouse in New Hampshire hints at the national importance of the elements bound inside the mining waste stored in 1-ton bags. The company uses electrolysis to separate the key critical elements President Donald Trump's administration desperately wants to produce domestically from the powder left behind at traditional mines. The small Phoenix Tailings refinery tucked inside an office park in Exeter, New Hampshire, could play a key role in helping America break the chokehold China has on the processing of critical minerals, but it will take 14 to 18 months to build a new factory with a $500 million loan from the Pentagon to drastically expand the company's separation and metallization capacity, a particularly weak stage in the U.S. mines-to-magnets supply chain. The task that workers carry out in heat-resistant suits and sealed face masks has become more urgent with the war in the Middle East rapidly drawing down munitions because critical minerals are a key ingredient in widely used U.S. weapons systems such as Tomahawk c