Is a concentration spell suppressed when the caster is in Antimagic Field?

Question

Antimagic Field, PHB, page 213:

Spells and other magical effects...are suppressed in the sphere and can't protrude into it...While an effect is suppressed, it doesn't function, but the time it spends suppressed counts against its duration.

The question remaining for this question, "Do any charm spells stop working when the caster is in an Antimagic Field?", is whether a spell a wizard is concentrating on is suppressed by Antimagic Field. The answers to the other question rely on the specific text indicating targeted creatures, "Any active spell or other magical effect on a creature or an object in the sphere is suppressed"; however, the general text is not considered. The answers to the other question also assume a "link" for telepathic effects, but if that is so, isn't there also a "link" for all concentration spells? My concern is the rule makers did not consider this, so it is a hole in the rules.

Exact scenario: Caster is concentrating on any spell that has an effect outside of the Antimagic Field, and then the caster enters the Antimagic Field. Is the spell he is concentrating on suppressed?

Note: Other questions answer whether the wizard is aware or whether his concentration ends (Do you know that Detect Magic is being suppressed if it intersects with Antimagic Field?, Does a spellcaster know when concentration ends?)

Answer 1

Your question is indirectly addressed by these tweets from Jeremy Crawford:

As DM, I'd rule that you can't control a delayed blast fireball while inside an antimagic field. ... You could regain control when neither you nor the bead was in the antimagic field.

Note that he's assumed the Delayed Blast Fireball spell doesn't get suppressed just because the caster is inside an Antimagic Field; however the intention (the rules are silent on this) is that you can't control a spell while you're in the antimagic field or while the spell is suppressed.

Answer 2

Jeremy Crawford mentioned in this sage advice that:

Antimagic field has no effect on concentration. If it did, its description would say so.

Additionally, in the 5e SRD concentration is defined as follows:

Some spells require you to maintain concentration in order to keep their magic active. If you lose concentration, such a spell ends

There is no mention anywhere that concentration is a magical effect. It is only the mechanism by which a magical effect is maintained. Additionally it is tied to the duration of a spell, but not to the effect of any spell.

As you have pointed out, Antimagic Field only suppresses spells and magical effects, which concentration all but explicitly is not.

Telepathic links are effects of a spell or magical effect, which is why they are suppressed in the field, but concentration is not an effect of a spell, or even really defined as a magical effect.

For all of these reasons, A concentration spell is not suppressed when the caster alone is in the Antimagic Field.