Where does Tomcat or Jetty saves the sessionids (without session persistence configuration)? Does it go anywhere in the file system, or does it stay just in memory?
Tomcat uses the StandardManager by default to manage it's session data. During run-time this data is not persisted to a store and exists only in memory. When you shutdown Tomcat it will try to persist all the session data to $TOMCAT_HOME/work/Catalina///SESSIONS.ser. Tomcat will try to reload these session on next startup and it will also delete the SESSIONS.ser file after a successful start. If your server dies or you execute a kill -9 this session data will be lost.
Documentation for the StandardManager is here http://tomcat.apache.org/tomcat-5.5-doc/config/manager.html
I don't know Jetty very well but Jetty does not have any persistence by default so the sessions are in memory. You can enable persistence if you want and its documented here docs.codehaus.org/display/JETTY/Persisting+Sessions.
Hope this helps.