Since you're working with fasta files, consider becoming familiar with Bio::SeqIO--a module that's a powerful tool for working with fasta and other such formats.

For example, to achieve your desired results using the module, you can do the following:

use strict;
use warnings;
use Bio::SeqIO;

my $in  = Bio::SeqIO->new( -file => 'file1.fasta',  -format => 'Fasta'
+ );
my $out = Bio::SeqIO->new( -file => '>file2.fasta', -format => 'Fasta'
+ );

while ( my $seq = $in->next_seq() ) {
    my $newSeq = Bio::Seq->new(
        -display_id => $seq->id,
        -seq        => 'aaaa' . $seq->seq
    );
    $out->write_seq($newSeq);
}
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Output results:

>dddd
aaaaabcdef
>eeee
aaaabcdef
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Notice that the module permits you to access sequences and ids as objects, using the "->" notation. For example, in the above, we prepend "aaaa" to the original sequence by doing the following:

'aaaa' . $seq->seq
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Then, create a new object with the modified sequence that's written to a new file.

The module offers many more options for working with fasta (and other similarly formatted) files.

Hope this helps!