sudo into root with a tmux session, default to a new session named with the date. Otherwise, do sensible things (ls will list root tmux sessions).

root_tmux.sh

# this will open up a root prompt inside a tmux session
# if nothing is given, open up a new tmux session with current datetime
# if a string is given, attach or new depending on if the session already exists
# Note: this will probably cause trouble if multiple people are using it.  Recommend
#       namespacing the sessions with your username.
function root () {
  name=$1
  session="new -s"

  if [ -z "$name" ]; then
    name=$(date +%Y-%m-%d-%H%M)
  elif [ "$name" = "ls" ]; then
    unset name
  elif [ -n "$(sudo -i tmux ls -F "#S" | grep "^$name")" ]; then
    session="attach -t"
  fi


  if [ -n "$name" ]; then
    cmd="tmux $session $name"
  else
    cmd="tmux ls"
  fi

  echo $cmd
  sudo -i $cmd
  unset name session
}