How to access instance variables in CoffeeScript engine inside a Slim template

What's happening is that "#{@user_name}" is being interpreted as CoffeeScript, not as Ruby code that's evaluated and injected into the CoffeeScript source. You're asking, "How do I inject a Ruby variable into my CoffeeScript source?"

The short answer is: Don't do this. The Rails team made an intentional decision not to support embedded CoffeeScript in templates in 3.1, because there's significant performance overhead to having to compile CoffeeScript on every request (as you'd have to do if you allowed arbitrary strings to be injected into the source).

My advice is to serve your Ruby variables separately as pure JavaScript, and then reference those variables from your CoffeeScript, e.g.:

javascript:
  user_name = "#{@user_name}";
coffee:
  $(document).ready ->
    name = user_name
    alert name

I tend to avoid inline javascript at all costs.

A nice way to store variables in your HTML, to be used from your javascript, is to use the HTML5 data-attributes. This is ideal to keep your javascript unobtrusive.

You could also use:

$(document).ready ->
  name = <%= JSON.generate @user_name %>
  alert name

This is because JSON is a subset of JavaScript.