What is the distribution of "absolute value of sum of N gaussian random variables with mean 0 and variance non-zero"?

Question

I know that for N = 2, we have $ \sqrt{X^{2} + Y^{2}} \sim \mathrm{Rayleigh}(\sigma) $, where $X \sim \mathcal{N} (0,\sigma^{2}) $ and $Y \sim \mathcal{N} (0,\sigma^{2}) $ but what about the following? $$ R = \left| \sum_{i=1}^{N} X_{i} \right| $$ where each $ X_{i} \sim \mathcal{N} (0,\sigma^{2}) $.

Please guide me on how to proceed? I searched the web but found nothing. Thanks in advance.