Alonso will start Sunday's IndyCar race from fifth for McLaren Honda Andretti, and produced his best F1 qualifying performance of the year by taking seventh on the grid in the Spanish Grand Prix earlier this month.
Brown believes that since the Indy deal was agreed shortly before April's Bahrain GP weekend, it has had a positive effect on Alonso, who has had a strong start to the season in terms of extracting the most from an uncompetitive package.
"A lot of driving is mental, and this has put him in such a great frame of mind that I think is very healthy," Brown told Autosport when asked about the impact on Alonso's performance in F1.
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Fernando Alonso is seen during practice for the Indianapolis 500 at Indianapolis Motor Speedway on May 15, 2017 in Indianapolis, In.

Image credit: Getty Images

"He feels good that he's racing, he's competitive, he's getting a lot of attention. He's not an attention seeker, but it's got to be fun knowing the world's watching you race.
"We all work best in a good frame of mind, whatever that job is. This has just got him in a really good place after two years of not being in a good place, as we haven't. It's had the same effect on the team and partners. It's just a breath of fresh air."
Brown says that, while Alonso's Indy achievements so far do not surprise him personally, the double F1 champion has still exceeded expectations.
"It is and it isn't a surprise - someone of Fernando's calibre you expect to do what he has done," said Brown when asked about Alonso's performance at Indy.

Fernando Alonso is seen during practice for the Indianapolis 500 at Indianapolis Motor Speedway on May 19, 2017 in Indianapolis, In.

Image credit: Getty Images

"However, this place is so difficult and tricky that usually even the world's best have a bad day. And, knock on wood, he's not had a bad day yet.
"He's showing he's a two-time world champion and further putting a stamp on his greatness. This is only going to make him a better driver.
Brown added that Alonso has taken to the IndyCar environment well both on and off track.
"He likes it, he's very settled into the IndyCar way of racing, of fan engagement, he's very relaxed and enjoying it. Nothing's bothering him, he's just having fun."
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