MarjorieRosenbe and thought I'd respond in a blog post:
The definition I present to my L2 learners is that a writer is one who writes. That's it - a painter paints, a carpenter drives, nails, a driver drivers, and so on. What I ask them to do is what many other L1 writers do: brainstorm, outline, free write, complete graphic organizers, etc. I explain that their first draft will never be good enough, so they should integrate several revisions into their own personal writing process. That is, the process of reaching the final written product is a unique journey that L2 writers learn to dictate for themselves. Also, I allow time for self and peer-assessment so that there are reflective and cooperative moments for learning, understanding that not every student will or should follow identical trajectories.
An L2 writing approach that focuses more on process than product over time will provide the basis for language learners to begin feeling like writers. It takes constant reminding and encouragement and the simple idea that what language learners are doing is just what many other writers do. The final component to the question, What does an authentic writer feel like? is what could I possibly mean by the notion of authentic.
My perhaps over simplified definition of authentic is what people tend to do in real life, usually outside of a forced learning environment typically found in many schools. Examples might be those who have a profession or vocation or it might be any purposeful activity that contributes to a greater good. Purposeful writing connects the (L2) writer to a real audience (and not just the language educator). Due to the sometimes difficulty in implementing a truly authentic learning environment in school, I tend to think of the term authentic as following along a non-authentic-fully authentic continuum. Indeed, the idea is to make the educative experience as authentic as possible. L2 writers who find purpose in what they do are more likely to actively participate.
In summation, instead of trying to define what an authentic writer should feel like, then attempt to pass this along to students, I begin with a simpler premise: What you do defines you. L2 writers doing what other (L1) writers do, makes them a writer. Writers don't just write as an academic exercise usually, but rather they have a purpose or a problem and real audience they must consider. My job as a language educator is to design learning experiences that allow L2 writers to realize that they are no different than L1 writers in that they are experiencing the same frustrations and joys that other writers feel. As they systematically learn how to overcome the frustrations of writing, they will begin to truly see what an authentic writer feels like.