Russian scientists are planning to reach Mars in record time i.e almost 45 day, using nuclear reactions. It's essentially Russia's national nuclear corporation, Rosatom, that has come up with this idea for a nuclear-powered spaceship, and it's not a entirely new notion either: both Russia and the United States were working on alike methods throughout the Cold War of the 1960s and onwards, however their plains were focused on lightweight orbital satellites instead of rockets to take us to Mars and back again.
But there is one big drawback in this, it’s very expensive. The really expensive thing about this plan will be designing a ship around these things, as Nikolai Sokov, senior fellow at the James Martin Centre for Nonproliferation Studies in California, told Wired.
While folks from Rosatom's haven't shared the detail about how the company's technology will work, it's likely to be some sort of thermal fission, where the heat of splitting atoms will be used to burn hydrogen or start another chemical, providing thrust for the spaceship. It's somewhat same in principle to chemical propulsion, where one chemical (the oxidizer) burns the other (the propellant) to power a vehicle along.
According to the company, a prototype will be prepared for flight testing in 2018. Nick Stockton from Wired says that Rosatom has only budgeted 15 billion rubles for the project, nearly US$700 million, which he calls "eyebrow-ravishingly inexpensive for a 15-year long space project". For contrast, he adds, NASA's Space Launch System is expected to cost nearly $10 billion.
So I think we'll just have to wait and see what those Russian rocket scientists are capable of in the next few years.