To go further, we can steal xE#'s idea and introduce the double-tilde!
a~~b = a~a~a~a~a... with b a's
This is growth rate of w^2, but we can go further.
a~~~b = a~~a~~a~~a... with b a's
a~~~~b = a~~a~~a~~a... with b a's
Limit is n~~~...n tildes...~~~n, which corresponds with omega^omega
Let's throw an extra rule in, then!
A represents any separator, a separator being a string of tildes
a~b = a^b
a~b~c = a^^^...c...^^^b = a{c}b
a A ... A b A 1 = a A ... A b
a A ... A b A 1 A c = a A ... Ab
a A ... A b [d] c = a A ... A b[d-1]b[d](c-1) where [n] represents n tildes in a row
a~...~b~c~d = a~...~b~(a~...~b~(c-1)~d)~(d-1)
This is equivalent to Cookie Fonster's extension of Chained-Arrow Notation, which reaches w^w on the FGH. So, it's safe to say this does too.
n~~n ~ w^2
n~~n~2 ~ w^2+1
n~~n~n ~ w^2+w
n~~n~n~n ~ w^2+w2
n~~n~~n ~ 2w^2
n~~n~~n~~n ~ 3w^2
n~~~n ~ w^3
n~~~~n ~ w^4
n[n tildes] n ~ w^w
Tildoodol = 10~~100
Great Tildoodol = 10~~100~2
Dutildoodol = 10~~10~100
Tritildoodol = 10~~10~10~100
Deutero-tildoodol = 10~~10~~100
Trito-tildoodol = 10~~10~~10~~100
Tildootrol = 10~~~100
Tildootetol = 10~~~~100
Tildoopetol = 10~~~~~100
Tildoodekol = 10~~~~~~~~~~100
Tildoohectol = 10[100 tildes]100