I don't think there is a way to accomplish exactly what you are trying to do (saving the individual tokes from one field into another), but if you just want to inspect how a particular field was processed you can cheat and use the facets to get this information.
For example, let's say that I have a Text field with the following information on a document with id "00000004":
"id":"00000004",
"title_txt_en":"Personal rights and the domestic relations /
Then I can output the individual tokens stored in title_txt_en for this individual record by faceting by this field using a query like this:
# q=id:00000004
# facet.field=title_txt_en
# f.title_txt_en.facet.mincount=1
curl http://localhost:8983/solr/your-core/select?f.title_txt_en.facet.mincount=1&facet.field=title_txt_en&facet=on&q=id%3A00000004
The response will include the following:
"facet_counts":{
"facet_queries":{},
"facet_fields":{
"title_txt_en":[
"domest",1,
"person",1,
"relat",1,
"right",1]}
where you can see the individual tokens that were indexed: "domest", "person", "relat", and "right" for this field in this record.
As I said, not an exact answer to what you are looking for, but hopefully it helps.