Using jqery you can do it the following way:

The ajax call should look something like this:

Code:
			$.ajax({
			  type: "POST",
			  url: "http://www.yourserver/your_php_file.php",
			  data: "data1=whatever&data2=whateverelse",
			}).done(function( msg ) {
			  $('#id_of_textarea').text($('#id_of_textarea').text() + msg);
			});
Inside your php file you simply return via "echo" waht you want to fill in.

Regards
PA